A bibliographic view on recurrence plots and recurrence quantification analyses

TL;DR

This paper provides a bibliographic analysis of recurrence plots and quantification methods, highlighting the field's growth, evolving topics, and collaborative research efforts over time.

Contribution

It offers a comprehensive bibliometric overview of recurrence plot research, revealing development trends, key contributors, and topical dynamics.

Findings

Field's popularity has steadily increased over time.

Emergence and decline of specific research topics identified.

Active collaboration networks among research groups.

Abstract

A bibliographic database containing studies on recurrence plots and related methods is analyzed from various perspectives. This allows a detailed view of the field's development, showcasing the continuous growth in the method's popularity, as well as the emergence, decline, and dynamics of topical subjects over time. Furthermore, the analysis unveils the activity and impact of the different groups, shedding light on their collaborative efforts and contributions to the field.

Tables

Table 1. Table 1: Size and components of the database (excluding papers before 1987 and entries classified as “related” and “software”).

Total number of authors	9272
Total number of papers	4778
Papers analysed	4563
Journal papers (incl. preprints)	3656
Proceedings	712
Books chapters (ed.)	174
Books	22
Thesis (Bachelor, Master, PhD)	33
Techreports	4
Number of different journals	1855
Total number of citations	31,118
Number of authors’ affiliations	3153
Countries of authors’ affiliations	101

Table 2. Table 2: Top journals and selected high prestigious journals publishing in the recurrence plot field, with total number of publications and fraction (in %) on all published works.

	Journal	Publications	Fraction
1	Chaos	166	3.79
2	Physical Review E	82	1.87
3	Chaos, Solitons & Fractals	67	1.53
4	International Journal of Bifurcation and Chaos	58	1.32
5	Physica A	56	1.28
6	Physics Letters A	53	1.21
6	Scientific Reports	53	1.21
7	Lecture Notes in Computer Science	50	1.14
7	European Physical Journal – Special Topics	50	1.14
8	Entropy	48	1.10
9	Nonlinear Dynamics	43	0.98
9	PLoS ONE	43	0.98
9	Sensors	43	0.98
10	Biomedical Signal Processing and Control	35	0.80
11	Frontiers in Psychology	34	0.78
12	IEEE Access	29	0.66
13	IEEE Sensors Journal	26	0.59
14	Europhysics Letters	25	0.57
	⋮
28	Proceedings of the National Academy of Sciences	7	0.16
28	Physical Review Letters	7	0.16
29	Heliyon	6	0.14
29	Nature Communications	6	0.14
31	iScience	4	0.09
32	Science Advances	3	0.07
34	Nature	1	0.02
34	Science	1	0.02

Table 3. Table 3: Clusters based on the titles, abstracts, and keywords of the paper in the database. Based on the 15 top features (words), subjects have been assigned to the clusters.

Cluster	Subject	Papers	Top words
1	Nonlinear Time Series Analysis	586	timeseries, data, recurrenceplot, dynamic, recurrence, nonlinear, dynamical, application, time, complex, recurrencequantification, model, information, structure, measure
2	Social Interaction Dynamics	364	coordination, interaction, movement, task, social, eye, participant, interpersonal, team, synchrony, human, behavior, dynamic, recurrencequantification, cross
3	Signal Detection in Monitoring Tasks	360	signal, detection, vibration, recurrenceplot, monitoring, damage, recurrencequantification, feature, frequency, recurrence, technique, time, power, condition, algorithm
4	Recurrence Plots as Features for Machine Learning	354	image, neuralnetwork, classification, convolutional, cnn, deeplearning, feature, accuracy, model, data, recurrenceplot, recognition, timeseries, deep, signal
5	Nonlinear Dynamical Systems	340	chaos, dynamic, exponent, lyapunov, attractor, nonlinear, dynamical, bifurcation, periodic, timeseries, recurrenceplot, model, motion, transition, dimension
6	Nonlinear Feature Extraction	276	recurrence, corrosion, recurrenceplot, noise, process, recurrencequantification, parameter, entropy, determinism, value, dynamic, line, surface, rate, current
7	Biomechanics, Motor control, and Neuromuscular Physiology	247	muscle, postural, control, emg, surface, group, subject, recurrencequantification, motor, healthy, determinism, balance, movement, signal, nonlinear
8	Cardiovascular Physiology	240	heart, rate, variability, hrv, cardiac, autonomic, nonlinear, patient, ecg, cardiovascular, interval, signal, time, recurrenceplot, subject
9	Brain Activity and Cognitive Science	215	brain, eeg, activity, functional, state, signal, cognitive, subject, recurrence, patient, dynamic, nonlinear, measure, potential, network
10	Epileptic Seizure Detection	208	eeg, feature, classification, signal, seizure, epileptic, classifier, accuracy, svm, detection, recurrencequantification, nonlinear, disorder, extracted, patient
11	Studies in Climate, Earth science, and Astrophysics	197	climate, solar, temperature, record, cycle, change, variation, period, year, long, event, dynamic, oscillation, time, activity
12	Fluid Flow Characteristics in Pipelines	166	flow, gas, bed, phase, water, pressure, velocity, pattern, fluctuation, oil, recurrenceplot, recurrence, signal, characteristic, dynamic
13	Recurrence Networks	151	network, recurrencenetwork, complex, timeseries, dynamical, property, dynamic, measure, graph, phasespace, recurrence, nonlinear, chaos, data, world
14	Classifying Dynamical System Types	150	deterministic, stochastic, chaos, dynamic, timeseries, nonlinear, data, process, recurrenceplot, model, noise, recurrencequantification, signal, component, dynamical
15	Synchronisation and Transition Analysis	145	synchronization, phase, coupling, coupled, oscillator, network, recurrence, chaos, cross, transition, time, state, probability, nonlinear, different
16	Combustion Processes & Thermoacoustic Instability	132	combustion, instability, thermoacoustic, flame, oscillation, pressure, acoustic, dynamic, transition, flow, cycle, amplitude, ratio, fluctuation, rate
17	Fault Diagnosis in Mechanical Systems	125	fault, diagnosis, bearing, vibration, signal, recurrenceplot, feature, neuralnetwork, image, condition, model, accuracy, convolutional, detection, data
18	Financial Market Analysis	108	market, price, financial, timeseries, index, chaos, recurrenceplot, dynamic, data, energy, recurrencequantification, time, behavior, nonlinear, correlation
19	Protein Structure & Folding Analysis	80	protein, sequence, structure, structural, recurrencequantification, prediction, class, feature, property, region, interaction, recurrence, information, set, function
20	Atrial Fibrillation Prediction	72	atrial, af, fibrillation, ecg, patient, recording, pattern, signal, recurrence, length, feature, recurrencequantification, cycle, clinical, cardiac
21	Monitoring and Prediction in (Road and IT) Traffic Networks	47	traffic, network, flow, anomaly, detection, statistical, data, short, term, prediction, detect, dynamic, recurrence, recurrencequantification, recurrenceplot

Table 4. Table 4: Papers cited more than 200 times ( C all C_{\mathrm{all}} ) and more than 9 times during the first two years after publication ( C 2 C_{2} ), considering only citations by the other papers in the recurrence plot database (ranked regarding the overall number of citations). Only citations within the RP/RQA community are considered.

	Paper ID	Call	C2	Reference
1	marwan2007	2404	68	[2]
2	eckmann87	2297	0	[1]
3	webber94	985	1	[5]
4	zbilut92	782	1	[4]
5	marwan2002herz	669	7	[6]
6	marwan2002pla	342	6	[57]
7	trulla96	318	0	[33]
8	marwan2009b	242	7	[7]
9	zbilut98	226	0	[34]
10	marwan2011	220	8	[58]
11	marwan2008epjst	208	3	[3]
12	donner2010b	206	15	[8]
20	donner2011	144	13	[53]
21	webber2015	143	12	[51]
29	zou2019	100	29	[9]
48	donges2012	59	10	[54]
52	donner2010a	54	13	[52]
74	mathunjwa2021	30	11	[55]
87	marwan2023	17	15	[11]
87	zhang2022	17	10	[56]

Table 5. Table 5: Number of publications P P , number of total citations C C , and average citations per paper A A of the top ten institutions (regarding the number of publications) and (additionally) the institutions with more than 40 publications or more than 500 average citations per paper. Only citations within the RP/RQA community are considered (the total number of citations is much higher).

	Institute	P	C	A
1	Potsdam Institut fur Klimafolgenforschung	191	3703	19.39
2	Humboldt-Universität zu Berlin	129	3062	23.74
3	Universität Potsdam	109	6554	60.13
4	Politechnika Lubelska	85	464	5.46
5	Tianjin University	82	397	4.84
6	Indian Institute of Technology Madras	72	523	7.26
7	University of Aberdeen	68	1166	17.15
8	University of Cincinnati	60	691	11.52
9	Istituto Superiore Di Sanita	56	950	16.96
10	Rush University	55	2629	47.80
11	Sapienza Università di Roma	51	693	13.59
12	Universidade Federal do Parana	49	292	5.96
13	Loyola University Chicago	47	3452	73.45
27	Université de Genève	3	2257	752.33
28	Institut des Hautes Études Scientifiques	2	2272	1136.00

Table 6. Table 6: Authors publishing at least for 20 years on recurrence plot based methods. The duration of publications is based on the final publication date, not the submission date, and may include posthumous publications.

	Author	Duration
1	Webber, Jr., C. L.	33
2	Kurths, J.	32
3	Kaplan, D.	28
4	Giuliani, A.; Balasubramaniam, R.	27
5	Schulz, S.; Orsucci, F.; Marwan, N.; Kankaanpää, M.; Dong, F.; Airaksinen, O.	26
6	Zimatore, G.; Schmidt, J.; Riley, M. A.; Hu, Z.; Banerjee, S.	25
7	Santarcangelo, E. L.; Faure, P.	24
8	Zbilut, J. P.; Trulla, L. L.; Strozzi, F.; Newell, K. M.	23
9	Trauth, M. H.; Pereda, E.; Li, X.	22
10	Wang, X.; Meng, Y.; Matcharashvili, T.; Liu, Y.; Liu, X.; Liu, C.; Litak, G.; Li, J.; Hatzopoulos, S.; Chen, H.; Chelidze, T.; Acharya, U. R.	21
11	Zou, Y.; Zhang, L.; Yao, X.; Wang, W.; Patel, M.; Lu, S.; Lu, H.; Liu, G.; Li, Y.; Li, M.; Keogh, E.; Huang, Y.; Faust, O.; Czarnigowski, J.; Chen, W.; Cerutti, S.	20

Table 7. Table 7: Largest communities in the co-author network (consisting of at least 1% of all co-authors), together with their first three most productive authors, the size (number of co-authors) of these communities, and the corresponding fraction on all authors (in %).

Comm.	Leading authors	Size	Fraction
574	Wang, Y.; Wang, J.; Wang, X.	1246	13.4
24	Marwan, N.; Kurths, J.; Donner, R. V.	467	5.0
32	Riley, M. A.; Shockley, K.; Turvey, M. T.	281	3.0
16	Zbilut, J. P.; Giuliani, A.; Webber, Jr., C. L.	255	2.8
937	Wallot, S.; Cox, R. F. A.; Hasselman, F.	222	2.4
567	Yang, H.; Chen, Y.; Bukkapatnam, S. T. S.	183	2.0
790	Lee, S.; Park, J.; Singh, A.	180	1.9
950	Acharya, U. R.; Faust, O.; Alcaraz, R.	174	1.9
628	Li, X.; Soriano, D. C.; Varni, G.	152	1.6
879	Lopes, S. R.; Prado, T. D. L.; Viana, R. L.	144	1.6
380	Litak, G.; Mosdorf, R.; Syta, A.	126	1.4
582	Pham, T. D.; Mukherjee, S.; Li, Q.	124	1.3
702	Hirata, Y.; Aihara, K.; Gotoda, H.	122	1.3
362	Sujith, R. I.; Sarkar, S.; Pawar, S. A.	112	1.2

Full text

1 Introduction

Quantitative methods to investigate recurring phenomena in theoretical and real world applications has become popular in the last decades. One promising and successful framework is based on the recurrence plot [1, 2], a tool to visually represent the temporal recurring patterns of a phase space trajectory of a dynamical system. It has its roots in nonlinear dynamics and complex systems [3], but extensions and further methodological developments were also contributed from other quantitative scientific fields. Quantitative extensions include recurrence quantification analysis [4, 5, 6], now a major foundation in this analytical framework, as well as recurrence networks [7, 8, 9], an example of fruitful combination of different fields (i.e., recurrence analysis with complex networks). Further methods and concepts very similar to recurrence plots have been developed independently, e.g., recurrence period density entropy [10].

The success of the recurrence plot based framework has been demonstrated by an impressing collection of exciting applications in different scientific disciplines [3, 11], ranging from classical applications in life science, like analysing cardiac diseases [12, 13, 14] and neurological disorders [15, 16, 17], cognitive sciences and psychology [18, 19, 20], engineering [21, 22, 23, 24, 25], to Earth sciences [26, 27, 28, 29].

Since more than 20 years, we maintain a project to get a bibliographic overview on the methods of recurrence plots, recurrence networks, recurrence quantification analysis, and related concepts [30]. Examining bibliographic data from various perspectives can enhance our comprehension of the historical evolution of a scientific field and aid in shaping future directions [31]. In this study, the bibliographic data available at [30] is analysed, to define the different fields where the recurrence plot framework found applications, to find communities of collaborations and different disciplines, and to understand the evolution of the different techniques and concepts which are now a strong integral part of the methodological framework.

2 Database

A database of scientific papers using recurrence plots, recurrence quantification analyses, and recurrence networks is curated by the author since more than 20 years (Tab. 1). Unfortunately, an exact start of the database cannot be reconstructed anymore, but the Internet Archive reveals one of the first versions in 2003 with 125 references [32]. The database is a BibTeX file. It includes articles, conference proceedings, books and book contributions, a few PhD thesis, as well as some of the available software, in total 4778 entries (by February 2025). Among them, the database includes a few papers which are related to recurrence features in dynamical systems or alternative approaches looking at recurrences, but not using the above mentioned methods which have their roots in the work by Eckmann et al. [1]. In the following analysis, these related papers and the software entries are neglected, as well as all entries before 1987. Papers in press are considered as published in 2025, although the final publication year could still be different. The resulting bibliographic data set has size $N=4563$. It is likely that it misses a few publications which are not easy to find.

The database is monthly updated. The update is based on citation alerts from Clarivate’s Web of Science and Elsevier’s Scopus services and manual curation. In the last six years, on average 35 new studies join the database per month (Fig. 1). The data used in this analysis is as of the February 2025 update of the data.

For the citation analysis, the services of Crossref and Semanticscholar are both utilised to retrieve the cited works within each paper. While both services are valuable, they can occasionally introduce slight uncertainties, for example, some references may be missing or incorrect in a few papers. It has also been observed that following a new run of the Crossref retrieval script, certain references were no longer included. To mitigate these issues, both services are used simultaneously. However, minor errors may still persist despite these efforts.

Affiliations for all authors of each paper are retrieved from Scopus. Here, not all affiliations could be automatically retrieved and are, thus, missing (401 missing from 4563 records, corresponding to 9% of the papers in the database). Furthermore, some minor errors have been found and corrected. For example, if there were obvious mistakes or differing names for the same institution, these were consolidated (e.g., “Rush Medical College” and “Rush University Medical Center” were renamed to “Rush University”, “Loyola University Stritch School of Medicine” and “Loyola University Medical Center” to “Loyola University Chicago”, and “Leibniz-Gemeinschaft” to “Potsdam-Institut für Klimafolgenforschung”). Nevertheless, despite missing a few affiliations and the possibility of encountering some minor glitches in institution names, the retrieved affiliations are deemed to be representative of the entire database.

Author names in the database comprise only the surname and the initials of the first name. This can pose challenges, as some authors may appear in the database with slightly different name variations (e.g., with or without a middle initial), or author names in the database may belong to different individuals (particularly with Chinese names, which present a major challenge). While some of these issues can be resolved, it may not be possible to address them comprehensively across all cases.

The corresponding scripts for these purposes are available on the mentioned link in the Data availability section.

3 Bibliographic analysis

3.1 General overview

3.1.1 Publications per year.

Although very similar concepts like recurrence plots existed before the seminal paper by Eckmann et al. [1], we consider here this paper as the first one and do not look further back (Fig. 2). Including the current year, we have 38 years of publications (but last year not shown). In the first ten years, only a few papers were published. In 1997, more than ten papers appeared for the first time in one year. Now, the numbers increased quite quickly, with reaching the milestone of more than 100 papers per year again almost ten years later (in 2008), 200 in 2015, and 300 in 2019. After 2019, the almost exponential grow in publication numbers stoped. Only a slight increase can be found for the last four years. This is a bit surprising, as we will see later (Subsect. 3.2), a new community has discovered recurrence plots and is making great use of this method and publishing a lot (hence, expecting a more rapid increase).

When delving deeper into the details of the exponential growth, it becomes evident that the rapid expansion of the field began to slow down significantly earlier, around 2008 (Fig. 3). The rate of growth was then more than halved. The next change occurred around 2019, when the growth rate was thirded. The larger growth rate in the first years (until around 2008/2009) can be understand by the rapid methodological developments and introduction of novel concepts, like recurrence quantification analysis [5, 6], time-dependent recurrence analysis [33], cross and joint recurrences [34, 35], interpretation of line structures and curved patterns [36, 37], or recurrence networks [7, 8]. From a methodological point of view, the last 15 years have witnessed less fundamentally new concepts – although they do exist (e.g., [38, 39, 40, 41, 42]) – but rather a proliferation of consolidations and robust mathematical underpinnings of the method, which obviously need more time to be worked out, e.g., [43, 44, 45, 46].

3.1.2 A growing community.

Similar to the number of publications per year, the number of authors per year and the number of new authors per year are important indicators for the interest and acceptance of a method. The number of authors and new authors per year is steadily increasing until 2021 (Fig. 4). In the last three years, these numbers seem to confirm some kind of saturation within the field, although we still see new scientists working with recurrence plots and related methods. For most of the time, the fraction of new authors is mainly in the range between 60 and 70%, with strong deviations in the first few years and a remarkable peak in 1997, when the interest obviously started to grow rapidly. In the last two years the interest seems to decrease a bit and the fraction of new authors dropped to 60%.

The cumulative sum of the new authors over the years corresponds to the size of the scientific community working with recurrence plots and related methods (Fig. 5). In the first six years, the community is quite small with less than 20 scientists. After the sixth year, the community grows exponentially, with extending the size 100 by 1998, and 1000 by 2008 (by February 2025, we have 9272 authors). In general, this exponential growth could be expected to be similar to the number of published works. However, we find different change points when comparing to the number of publications. In the first ten years, the community experiences its fastest growth. After around 1997, the growth rate declines and after 2009, it further decreases. This latter change point corresponds more or less to the change of the exponential growth in the number of publications and the possible reasons as explained above.

3.1.3 Journals publishing in the field.

The top journals which publish studies using recurrence plot based methods are mainly from the fields of physics, in particular on nonlinear and complex systems science, such as Chaos, Physical Review E, Physica A, Chaos, Solitons & Fractals, and International Journal of Bifurcation and Chaos (Tab. 2). Among the top journals are also some from more specific scientific disciplines such as biomedical and psychological sciences, and, a bit surprising, from a more engineering related field on applications of sensors: Biomedical Signal Processing and Control, Frontiers in Psychology, (MDPI) Sensors, and IEEE Sensors. PLoS ONE, Scientific Reports, and IEEE Access represent the only general journals in this top list, although others high prestigious journals have published studies using recurrence plot based methods, like Proceedings of the National Academy of Sciences (7), Physical Review Letters (7), Heliyon (6), and Nature Communications (6), or even Nature and Science (1).

The seminal paper on recurrence plots by Eckmann et al. was published in Europhysics Letters (EPL) [1]. However, this journal has not further received much attention from other authors publishing in this field (Fig. 6). Its popularity dropped down to position 14 in the year 2025 (Tab. 2). For more than a decade, Physics Letters A was the main journal for publishing recurrence plot papers. Between 2005 and 2015, Physical Review E and International Journal of Bifurcation and Chaos have published a lot. Since 2005 (first paper in 1998), Chaos is steadily increasing in the interest of authors. Since 2008 it is the journal which is publishing most of the works and after 2017 it received a jump in attracting papers on recurrence methods.

Other important journals in this field are, as mentioned before, Physica A, which has seen first recurrence plot papers in 2001, and Chaos, Solitons & Fractals, since 1995. Lecture Notes in Computer Science and European Physical Journal – Special Topics are often used for conference proceedings. Newer journals are PloS ONE, Scientific Reports, and Entropy. Since 2018, the number of papers in Sensors is rapidly growing, mainly with papers on recurrence analysis in combination with machine learning. The growth of journals like Frontiers in Psychology and Biomedical Signal Processing and Control in the field is an indication for a strong community in these disciplines which uses recurrence methods and that these methods have become established methods there.

3.2 Subject analysis

In order to get an overview on the different scientific disciplines, recurrence plot based methods are used in, subjects for each paper in the database should be assigned. Using a service like Crossref has not been useful for this purpose. The resulting subjects are too much overlapping and the resulting clusters of papers are not informative enough. An alternative would be a clustering analysis of the titles, abstracts, and keywords (when available). Here, a GMM (Gaussian mixture model clustering) clustering is applied. The words from the titles, abstracts, and keywords are merged for each paper and automatically and manually transformed into their base or dictionary form, reducing each word to its root form to facilitate analysis and comparison (lemmatization).

To find the optimal number of clusters, the criteria are that the clusters should not overlap too much (which is quite difficult when using titles and abstracts) but reflect meaningful subject-based clustering. The Davies-Bouldin index [47] and silhouette score [48] are used to numerically support the choice of an optimal cluster number. The Davies-Bouldin index measures the similarity between the clusters and the silhouette score evaluates how well-separated the clusters are. The Davies-Bouldin index indicates a better clustering with lower scores, whereas the silhouette score should have larger scores. Increasing the number from 1 to 50 clusters reveals a rapid decrease of the Davies-Bouldin index until a cluster number of 13 (Fig. 7). After this cluster number, the index decreases slower, with a small local minimum at 22. The silhouette score shows an almost linear increase up to 20, after which it levels off into a plateau. A cluster number of 21 seems quite appropriate and is a trade-off to have enough subject-specific clusters and only a low number of redundant clusters.

This analysis groups the papers into different subjects (Tab. LABEL:tab_clusters). The result is not perfect. Some clusters contain more than one subject (e.g., cluster 6 contains some more general time series analysis studies, but also papers on vibration monitoring), or even some subjects are missing or hidden within the dominating topic of a cluster. However, for a larger number of clusters, many redundant clusters appear, i.e., with very similar topics. Similar topics are already visible for the choice of 21 clusters (for larger cluster numbers the number of redundant cluster increases significantly), such as clusters 1, 3, 5, and 6; 3, 6, and 14; 3 and 17; 8 and 20; or 12 and 16.

The largest cluster (cluster 1) is on the subject of nonlinear time series with 586 papers, including the seminal paper by Eckmann et al. [1]. The second largest cluster (cluster 2) is on dynamics of social interactions. Several of the larger clusters (7 to 10) are related to life sciences (psychology, cognitive sciences, cardiovascular and brain physiology). This shows that there is solid community in these fields working with recurrence plot based methods. Similarly, engineering-related topics are spread over several clusters (3, 6, 12, 16, 17, 21). We further find clusters on financial markets and protein folding (clusters 18 and 119). Not to forget the rather new but rapidly growing field of machine learning-based classification approaches, which utilize recurrence properties as features in learning-based classification methods (cluster 4).

When applying the same clustering schema to a subset of the papers restricted by time intervals (from 1987 to a specific year), it is possible to study how selected subjects have evolved over time, when specific achievements were reached, or when hot topics emerged (Fig. 8).

Since the method is nonlinear time series analysis and has its roots in the fields chaos and dynamical systems, it comes as no surprise that clusters 1 and 5 are among the initial ones to emerge. Studies on cardiovascular and brain dynamics (clusters 7 and 8) were the first applications of this method; corresponding clusters start in 1990 and 1991. Next applications were found in neuromuscular physiology (1995) and protein structure analysis (1997). Interestingly, the latter subject peaked between 2000 and 2009, but gradually declining thereafter and showing a relative decrease in its community size within this field (in total numbers it is still increasing). Additional subjects can be identified along with their inception dates, e.g., recurrence network analysis (cluster 13), starting with 2006 and abruptly increasing in 2009, combustion analysis (cluster 16), strongly increasing around 2015, and early works on solar physics (cluster 11), starting 1994. Notably, cluster 4, focusing on feature-based classification and machine learning, has experienced rapid growth since 2014, signifying the onset of the machine learning hype after this year. Applications in engineering (clusters 12, 16, 17, 21) have started and expanded after the mid-2000ies.

3.3 Citation analysis

Paper citations serve as a measure of scholarly influence [49]. For such analyses, the references of all papers in the database are collected from Crossref and Semanticscholar (see Sec. 2) and used to find the citations of papers. This approach ensures that we only consider in-community citations and the influence of papers within the recurrence plot/ recurrence quantification field. In general, a paper may have received many more additional citations beyond those analysed here. Moreover, due to the found errors and inconsistencies in the Crossref and Semanticscholar database, the number might not be 100% accurate. In total, the papers in the database have cited each other 31,118 times.

The citation time of a paper, defined as the duration between its publication and when it garners citations, can serve as a metric for assessing the topicality of a subject. Papers that are frequently cited shortly after publication, typically within the same year or shortly thereafter, indicate a ‘hot topic’ or a high level of relevance and significance [50]. In the recurrence plot database, papers were mostly cited after two to four years (Fig. 9). After this time, the number of citations decreases the older the paper is. This decrease follows approximately an exponential decay, $e^{-0.07t}$. Only the most relevant papers are further cited.

The papers which were most frequently cited within the same or the next year are the review papers [2, 9, 8] and the edited book [51] (Tab. 4). These papers are also the ones which are cited for longer times. Among these most frequently cited papers within in the first year are further the topical papers on recurrence networks [8, 52, 53, 54] and on combining machine learning with recurrence approaches [55, 56]. These examples express well the very topical nature of these subjects.

Of the 4563 papers, 43% ($n=1971$) were not cited at all and about 57% were cited at least once (Fig. 10). 12% of the papers were cited at least 10 times, 6% were cited 20 times and 0.7% were cited 100 times. The top ten papers in this ranking have more than 200 citations. Among them, the two seminal papers [1, 2] received about 2200 citations each (Tab. 4).

For each year, we can identify the paper with the highest number of citations. Considering these data over time reveals peaks that highlight milestone works in the field (Fig. 11). Given that more recent papers tend to have fewer citations, we can identify the following significant milestones.

The first paper on recurrence plots by Eckmann et al. in 1987 [1] is, of course, one with the highest peaks. Following that, the introduction of the recurrence quantification idea in 1992 by Zbilut and Webber, along with the addition of additional measures in 1994 [4, 5], represent the next significant peaks. The approach of windowed recurrence quantification analysis by Trulla et al. in 1996 [33] is also discernible. A small peak in 1998 marks the introduction of the cross-recurrence idea [34]. The next notable peak appears in 2002 with the introduction of the recurrence quantification measures based on vertical lines [6]. In 2004 and 2005, small peaks emerge, associated with studies on estimating dynamical invariants from recurrence plots [59] and detecting phase synchronisation with an innovative bivariate extension of recurrence plots [60]. The highest peak occurs in 2007 when a review paper on the method was published [2]. Subsequent peaks in 2009 and 2010 correspond to the introduction of the recurrence network approach [7, 8]. The peak in 2011 is related to a critical paper highlighting potential pitfalls associated with the method [58]. Peaks in 2015 and 2019 are linked to an edited book on recurrence quantification analysis [51] and a review paper on network-based time series analysis [9], respectively. The small peak at 2018 indicates one of the first papers using RP-based time series imaging for machine learning [61].

3.4 Impact of Institutions

The activity and impact of institutions is represented by the number of publications and their respective citations. To avoid multiple counting within one paper, an institution is counted only once if co-authors from a paper are from the same institution. In total, the Scopus search for the affiliations of all authors in the database found 3153 different institutions. Unfortunately, the search was not successful for every paper, thus, the statistics is missing some counts (see Sec. 2). We should also remember that authors can change their affiliations due to moving to another institute, therefore, lowering or biasing the presented numbers for specific institutions. Some authors can also have more than one affiliation, thus contributing to more than one institution and further biasing the statistics (as, in particular, happened for the top ranked institutions as we will see below).

The most active institutions based on number of publications (considered as the top 10) over the entire time are mainly related to seven groups: the group at the (1) Potsdam Institute for Climate Impact Research (PIK), Humboldt University Berlin, University of Potsdam, and University of Aberdeen (these four institutions are associated with the group of authors around Kurths and Marwan; where Kurths was previously affiliated with the University of Potsdam and is currently affiliated with the Potsdam Institute for Climate Impact Research, Humboldt University Berlin, and the University of Aberdeen), (2) the Polytechnical University Lublin (group around Litak), (3) the Tianjin University (group led by Gao and Jin), (4) the Indian Institute of Technology Madras (group led by Sujith), (5) the University of Cincinnati (group led by Kiefer and Riley), (6) the Istituto Superiore Di Sanita and Sapienza University in Rome (group around Giuliani), (7) and Rush University and Loyola University Chicago (group around Zbilut and Webber, Loyola University Chicago is mentioned here although it is not in the top ten) (Tab. 5, column P). The three institutions with high numbers of publications – the Polytechnical University Lublin, the Tianjin University, and the Indian Institute of Technology Madras – are noteworthy because they are primarily associated with studies in the field of engineering science.

The citation analysis on the institutional level reveals the importance and impact of the institutions in this field (Tab. 5, columns C and A). Considering the average number of citations per paper, the Institut des Hautes Études Scientifiques and University of Geneve are the top institutions with more than 750 (and even 1000) citations per paper. These are the host institutions of the authors of the first paper on recurrence plots [1].

The next top institutions have more than 40 average citations per paper (but less than 100): Loyola University Chicago, Rush University, and University of Potsdam, with introduction of and major contributions on the recurrence quantification analysis [4, 5, 6], as well as the review paper on recurrence plots [2]. Average per paper citations of more than 10 are still quite remarkable and draw the Humboldt University Berlin, the Potsdam Institute for Climate Impact Research (PIK), the University of Aberdeen, Istituto Superiore Di Sanita in Rome, Sapienza University in Rome, and the University of Cincinnati to the most important institutions in the field.

3.5 Authors

The number of author’s publications and the duration authors remain active in publishing within the field serve as indicators of their experience and expertise. The majority of authors in the database has published only once (69%) and only in one year (73%; see Fig. 12), 29% of them have published as first author. The distribution of the duration authors are publishing follows an exponential decay $\sim e^{-0.19t}$. Less than 0.2% of authors have published at least 20 years (Tab. 6). Webber and Kurths have been active in the field for over 30 years, making them the longest-standing contributors. They are closely followed by Kaplan and Giuliani in terms of their duration of activity.

3.6 Collaborations

Finally, we consider the collaborations of the scientists in the fields of recurrence plots and recurrence quantification.

3.6.1 Country-level collaborations.

A general view can be achieved by looking at the countries of the authors (based on the affiliations, retrieved by Scopus). We find in total 101 countries with authors publishing on recurrence plots, where an author can have multiple affiliations in different countries, and therefore, could be counted several times. Among these countries are the US, China, Germany, India, UK, Italy, and Poland the most active countries (with more than 200 publications each). The collaboration network of the co-authors at the country level reveals strong collaborations between UK and Germany, US and Italy, Germany and US, China and US, UK and US, India and US, and UK and China, to mention the top collaborations based on the volume of joint papers produced (Fig. 13). We also observe widespread usage of the method across all continents, with Africa showing relatively fewer contributions and collaborations compared to other regions.

3.6.2 Co-author network.

A more detailed analysis can be performed on the co-author level. In average, a paper is written by four authors (median). The number of co-authors ranges from one to a maximum of 40 authors [62] (Fig. 14).

By constructing a co-author network, communities can be easily identified (Fig. 15). In general, the communities are formed by groups at universities (e.g., supervisor and students, project collaborators), and by specific disciplines (e.g., complex systems, cognitive science, life sciences, engineering). After applying a community detection algorithm [63], the largest communities (Tab. 7) are the ones led by Wang, X.; Wang, J.; and Wang, X. (community 574); Marwan, N.; Kurths, J.; and Donner, R. V. (community 24); Riley, M. A.; Shockley, K.; Turvey, M. T. (community 32); Zbilut, J. P.; Giuliani, A.; Webber, Jr., C. L. (community 16); and Wallot, S.; Cox, R. F. A.; Hasselman, F. (community 937). Most of the larger communities are mutually connected (probably due to more general methodological joint work), but others are more separated, e.g., communities 937 (Wallot and Cox et al.), 380 (Litak et al.), and 950 (Acharya et al.), probably because of some kind of topical specialisation. Nevertheless, the co-author network shows an impressive and close exchange of the different scientific fields, and a collaborative community. (A version of the co-author network including all authors with at least one co-author, i.e., at least with a network degree of one, is accessible in the Zenodo repository, with the link provided in the Data availability section.)

4 Conclusions

In this bibliographical study, we have examined the field of recurrence plot based analysis from different perspectives. While the analysis is grounded in simple statistical considerations, more sophisticated analyses could undoubtedly be conducted. Nevertheless, it already provides valuable insights into the dynamics of the field. There remains ample opportunity for further investigation and refinement in the future.

The available data covers almost 40 years. During this time span, we found a rapid growing interest in the field by a growing number of publications and a growing scientific community. The growth rate slightly decreased around 2009 (based on number of publications and size of community), albeit expressing still an exponentially (but slower) growing field. After 2019, we found another breaking point, which may indicate saturation or the reaching of a limit in the expansion of the method to different fields and scientific communities.

The major important journals in the field are mainly from physics, covering interdisciplinary physics, nonlinear dynamics, and chaos. But we also find some more general journals and high-ranked journals publishing studies based on recurrence analysis.

A cluster analysis has identified the scientific disciplines where recurrence plot based methods have found applications. These range from nonlinear time series analysis and dynamical systems theory, over several life science disciplines (cardiovascular, brain, cognitive, social sciences) and engineering (monitoring, damage detection, combustion optimisation), to financial markets and protein structure analysis. A remarkable new and quickly growing field is the combination of machine learning and recurrence plots for classification purposes. The analysis of these fields over time reveals their emergence and, for some fields, subsequent (minor) decline.

The citation analysis sheds light on the general citation dynamics. Papers are mostly cited after two to four years, but then gradually losing interest. The peaks in the number maximum citations over time indicate the milestones in the development of the recurrence based methods. Citation analysis also helps to identify the most active groups in the field.

Finally, collaborations on country-level and co-author-level are considered. This analysis reveals the main institutional and disciplinary communities active in the field. Moreover, it demonstrates an impressive and close exchange of the different scientific fields, and a highly collaborative community.

The field on recurrence plots, recurrence networks, and recurrence quantification analysis is lively and steadily growing. The rapidly expanding subject of machine learning is poised to become a major direction in the coming years.

5 Data availability

The used BibTeX file with the recurrence plot bibliography (as of February 2025 update) and scripts for data retrieval and analysis are available at Zenodo: https://doi.org/10.5281/zenodo.14904816.