Enhancement of synchronized chaotic state in a delay-coupled complex neuronal network

Synchronized firing of neurons is considered as one of the crucial characteristics for signal transmission and neuronal coding. In this article, spatiotemporal synchronization of coupled chaotic Chialvo maps is studied over a network where the connection topology changes at every time instance with chaotically changing rewiring probability. However, the main objective of this study is to investigate the effect of time delay in the ensemble behavior of neurons. As it is well known that delay is unavoidable in neuronal system, we introduce a delay parameter in the coupling term. Examining the bifurcation diagrams, we observe interesting changes in the synchronization behavior with the increment of delay. These results are complemented by the linear stability analysis of the synchronized state of the system using master stability function technique. Moreover, effects of time delay on synchronization behavior of the coupled system are investigated by evaluating average synchronization error and synchronization time. We observe non-monotonic variation of synchronization time with respect to coupling strength for non-delayed system, whereas this characteristic does not persist with the increment of delay. It is observed that the synchronized region of the considered model appears as a combination of homogeneous steady state and homogeneous chaotic state for both delayed and non-delayed systems. Our key finding in this study is the enhancement of synchronized chaotic region and consequently reduction of synchronized steady state with the increasing values of time delay in the system. Global stability of the synchronized state is examined by basin stability measure. It is also observed that depending on different values of delay, the system exhibits various spatiotemporal patterns.