Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation

Abstract

We study numerically effects of time delay in networks of delay-coupled excitable FitzHugh–Nagumo systems with dissipation. Generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh–Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established. It is shown that the emergence of an oscillatory activity in delay-coupled FitzHugh–Nagumo neurons is observed for smaller values of the coupling strength as the dissipation parameter decreases. This can provide the possibility of controlling the spatiotemporal behavior of the considered neuronal networks. The observed effects are quantified by plotting distributions of the maximal Lyapunov exponent and the global order parameter in terms of delay and coupling strength.

Strong delayed negative feedback

“…Networks of delayed coupled Kuramoto oscillators are popular dynamical problems because the state of an oscillator is described by a single angular variable ( Laing, 2016 ; Bick et al, 2020 ). Another simplification is to consider ring geometries of (unidirectional or bidirectional) coupled nodes ( Yuan and Campbell, 2004 ; Bungay and Campbell, 2007 ; Ibrahim et al, 2021 ; Bukh et al, 2023 ). But the main difficulty remains the fact that we are dealing with coupled delay differential equations (DDEs).…”