Asynchronicity yields regularity in coupled neuronal systems

Asynchronicity is a fundamental feature of dynamical evolution of complex interactive systems. In this work, we explore the impact of asynchronicity on the spatiotemporal dynamics in a system of coupled chaotic neurons. Our crucial finding is that asynchronicity can suppress neuronal oscillations under sufficiently strong coupling. For strong asynchronicity, one obtains complete cessation of neuronal activity in a very wide window of coupling strengths, while for weaker asynchronicity, neuronal activity is quenched over a smaller range of coupling. We also rigorously analyze a system of two coupled neurons for the distinct cases of synchronous updates, sequential updates, and random asynchronous updates. We find that our stability analysis is in complete agreement with results from numerical simulations, offering an underlying rationale for the effects of asynchronicity. We also analyzed the dynamics of large systems in a time-averaged framework. Our analysis yields values of critical coupling very close to those obtained from simulations.