On the analysis of a heterogeneous coupled network of memristive Chialvo neurons

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 not only varying 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 update the network topology with each iteration in time. We have further reported various rich spatiotemporal patterns like two-cluster states, chimera states, 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 a 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.