Transition from winnerless competition to synchronization in time-delayed neuronal motifs

Abstract

The dynamics of brain functional motifs are studied. It is shown that different rhythms can occur in the motifs when time delay is taken into account. These rhythms include synchronization, winnerless competition (WLC) and "two plus one" (TPO). The main discovery is that the transition from WLC to synchronization can be induced simply by time delay. It is also concluded that some medium time delay is needed to achieve WLC in the realistic case. The motifs composed of heterogeneous neurons are also considered.

Dynamics of Time Delay-Induced Multiple Synchronous Behaviors in Inhibitory Coupled Neurons

“…Different from the results of Refs. [ 27 , 29 ] wherein only the first of the multiple synchronous behaviors appears at time delays within 0 < τ < T and each of the remaining behaviors appears at time delay within ( n −1) T < τ < nT ( n = 2, 3), multiple synchronous behaviors in the present paper appear at time delay within 0 < τ < T . The multiple synchronous behaviors are period-( K − 2), period-( K − 1), period- K and period-( K +1) bursting patterns, which appear at different intervals of τ when coupling strength is suitable.…”

“…However, the relationship between time delays corresponding to the synchronous behaviors and the period of the bursting remained unclear. In another investigation, inhibitory coupled neurons have been shown to exhibit multiple synchronous behaviors in motif composed of three neurons or network, and each behavior appears at time delay of odd integer multiples of half of the endogenous firing period [ 27 , 29 ]. Only a single synchronous behavior appears when time delay is shorter than the period of the endogenous firing [ 27 , 29 ].…”

“…In another investigation, inhibitory coupled neurons have been shown to exhibit multiple synchronous behaviors in motif composed of three neurons or network, and each behavior appears at time delay of odd integer multiples of half of the endogenous firing period [ 27 , 29 ]. Only a single synchronous behavior appears when time delay is shorter than the period of the endogenous firing [ 27 , 29 ]. The simulation result of the first synchronous behavior is consistent with the observation of synchronous behavior from biological experiment on motif composed of two neurons with slow inhibitory synapses [ 24 ].…”

The influence of single neuron dynamics and network topology on time delay-induced multiple synchronous behaviors in inhibitory coupled network

“…Stable synchronous solution is obtained for long time delay in a pair of mutually inhibitory coupled neurons with self-inhibitory [45]. Time delay can induce transition from winnerless competition to synchronization [46]. Synchronous behaviors induced by time delay exhibit period-adding bifurcation [47,48].…”

“…However, inhibitory synapses can induce synchronization in some conditions with or without time delay [35][36][37][38][39][40][41][42][43][44][45][46][47]. Inhibitory synapses without time delay [35][36][37][38][39][40][41][42], for example, slow decay inhibitory synapses, can induce in-phase synchronization [35][36][37][38][39][40].…”