Multiple Stochastic Resonances and Oscillation Transitions in Cortical Networks With Time Delay

Abstract

Stochasticity and oscillation play a vital role in neural signal processing. Time delay, which is inevitable in biological neural systems, has significant effect on the dynamics of neuronal networks. This paper provides an analysis of how time delay affects stochastic resonance and firing rate oscillation of cortical neuronal networks. A cortical network is established and mean-field theory is applied to analytically compute the dynamical response of networks. When the frequency of external stimulation is close to intrinsic frequency of neuronal networks, firing rate exhibits coherent oscillation and the phenomenon of stochastic resonance occurs in inhibitory neurons. Time delay can induce multiple stochastic resonances, which appear intermittently at integer multiples of the period of input signal, due to the transition of network dynamics induced by time delays. The fluctuation of membrane potential and instantaneous firing rate of cortical networks achieve maximal periodically with the variation of time delay. Furthermore, time delay and electrical coupling play complementary roles in determining network responses. Network oscillation can transit from unstable to stable when coupling strength exceeds a critical value. Transition threshold is lower for time delays close to integer multiples of input period where resonant response of cortical network enhances the formation of stable oscillation.