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

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.