Synchronization patterns in a network of diffusively delay-coupled memristive Chialvo neuron map

Abstract

The inescapable presence of time delay in numerous real-world systems, particularly in neuronal networks, prompts an exploration of its impact on synchronization dynamics. This study employs memristive Chialvo maps to capture the local dynamics of network nodes, while connections are homogeneously described by a linear diffusive function—referred to as electrical couplings in mathematical neuroscience—incorporating a specific time delay. Using Master stability functions (MSFs), analytical assessments are conducted to examine the stability of synchronous solutions, a validation supported by time-averaged synchronization error calculations. This research reveals the time delay's influence on the synchrony, making the synchronous state dependent on the coupling parameter's strength. The behavior of the synchronization manifold is systematically probed across synchronous and asynchronous regions analyzed by the MSF analysis. Lastly, an investigation involving a neuronal network with a global coupling configuration reveals that neurons have a tendency to organize into clusters with distinct time lags.