Exotic states induced by co-evolving connection weights and phases in complex networks

TL;DR

This paper investigates how co-evolving connection weights and phases in adaptive complex networks, modeled by Kuramoto oscillators, lead to exotic dynamical states under external forcing, revealing new synchronization phenomena.

Contribution

It introduces a novel adaptive network model with co-evolving weights and phases, demonstrating the emergence of exotic states not seen in non-forced networks.

Findings

Discovery of itinerant chimeras and bump states induced by external forcing.

Development of measures to classify dynamical states based on frequency coherence.

Phase diagram illustrating diverse dynamical regimes in the parameter space.

Abstract

We consider an adaptive network, whose connection weights co-evolve in congruence with the dynamical states of the local nodes that are under the influence of an external stimulus. The adaptive dynamical system mimics the adaptive synaptic connections common in neuronal networks. The adaptive network under external forcing displays exotic dynamical states such as itinerant chimeras whose population density of coherent and incoherent domains co-evolves with the synaptic connection, bump states and bump frequency cluster states, which do not exist in adaptive networks without forcing. In addition the adaptive network also exhibits partial synchronization patterns such as phase and frequency clusters, forced entrained, and incoherent states. We introduce two measures for the strength of incoherence based on the standard deviation of the temporally averaged (mean) frequency and on the mean frequency in order to classify the emergent dynamical states as well as their transitions. We provide a two-parameter phase diagram showing the wealth of dynamical states. We additionally deduce the stability condition for the frequency-entrained state. We use the paradigmatic Kuramoto model of phase oscillators which is a simple generic model that has been widely employed in unraveling a plethora of cooperative phenomena in natural and man-made systems.