On the analysis of a time varying noise-modulated heterogeneous coupled network of Chialvo neurons under the influence of electromagnetic flux

TL;DR

This study numerically explores how electromagnetic flux influences a heterogeneous, noise-modulated network of Chialvo neurons, revealing complex spatiotemporal patterns and synchronization behaviors relevant to neural systems.

Contribution

It introduces a novel analysis of time-varying noise-modulated heterogeneity in Chialvo neuron networks under electromagnetic flux, highlighting diverse dynamical states and synchronization phenomena.

Findings

Identification of multiple spatiotemporal patterns including chimera states and traveling waves.

Discovery of solitary nodes exhibiting unique asynchronization behavior.

Quantitative analysis of network behavior using cross-correlation, synchronization error, and sample entropy.

Abstract

We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the central-peripheral and the peripheral-peripheral coupling links in the topology that not only vary in space but also in time. The variation in time is understood by two coupling probabilities, one for the central-peripheral connections and the other for the peripheral-peripheral connections respectively, that updates the network topology with each iteration in time. We have further reported the rich spatiotemporal patterns like two-cluster states, chimera states, traveling waves, coherent, and asynchronized states that arise throughout the network dynamics. We have also investigated the appearance of a special kind of asynchronization behavior called "solitary nodes" that have wide range of applications pertaining to real-world nervous systems. In order to characterize the behavior of the nodes under the influence of these heterogeneities, we have studied two different metrics called the "cross-correlation coefficient" and the "synchronization error". Additionally, to capture the statistical property of the network, for example, how complex the system behaves, we have also studied a measure called "sample entropy". Various two-dimensional color-coded plots are presented in the study to exhibit how these metrics/measures behave with the variation of parameters. Finally, how the nodes synchronize or asynchronize is shown via one-dimensional bifurcation diagrams of the last instance of the main dynamical variable, i.e., the state variable associated with the membrane potential, against different network parameters.