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

Abstract

The inhibitory synapse can induce synchronous behaviors different from the anti-phase synchronous behaviors, which have been reported in recent studies. In the present paper, synchronous behaviors are investigated in the motif model composed of reciprocal inhibitory coupled neurons with endogenous bursting and time delay. When coupling strength is weak, synchronous behavior appears at a single interval of time delay within a bursting period. When coupling strength is strong, multiple synchronous behaviors appear at different intervals of time delay within a bursting period. The different bursting patterns of synchronous behaviors, and time delays and coupling strengths that can induce the synchronous bursting patterns can be well interpreted by the dynamics of the endogenous bursting pattern of isolated neuron, which is acquired by the fast-slow dissection method, combined with the inhibitory coupling current. For an isolated neuron, when a negative impulsive current with suitable strength is applied at different phases of the bursting, multiple different bursting patterns can be induced. For a neuron in the motif, the inhibitory coupling current, of which the application time and strength is modulated by time delay and coupling strength, can cause single or multiple synchronous firing patterns like the negative impulsive current when time delay and coupling strength is suitable. The difference compared to the previously reported multiple synchronous behaviors that appear at time delays wider than a period of the endogenous firing is discussed. The results present novel examples of synchronous behaviors in the neuronal network with inhibitory synapses and provide a reasonable explanation.

Effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks

“…For phase synchronization of burst neurons, it has been found that at a certain noise intensity the onsets of bursts in different neurons could become phase synchronized. 17 Moreover, some factors such as coupling strength, [26][27][28] coupling forms, 29 diversity, 30 noise, 31 and especially time delay [32][33][34][35] could induce various phase synchronization transitions in neuronal networks.…”

Dynamic transition of neuronal firing induced by abnormal astrocytic glutamate oscillation

“…proposed an improved model to describe the emergence and transition of multiple modes in electric activities by introducing magnetic flux in the original Hindmarsh-Rose neuron according to electromagnetic induction effect 7 8 . Some intermediate neurons are connected with autapse, a specific autapse connected to the body of neuron, which counts the emergence of intrinsic time delay in neuron 9 . The previous works confirmed that autapse connection plays important biological function by regulating the electric activities of isolate neuron and collective behaviors of neuronal network as pacemakers 10 11 12 13 14 15 16 17 .…”

Different dynamical behaviors induced by slow excitatory feedback for type II and III excitabilities

“…Except for the autapse, excitatory or inhibitory effects such as external stimulation or coupling are identified to induce abnormal phenomena. For example, inhibitory stimulation can enhance neuronal firing 65,66 , and inhibitory coupling can enhance the firing frequency of a neuronal network [67][68][69] . Such results of abnormal activities of neural firings enrich the knowledge of neurodynamic and nonlinear dynamics.…”

“…Based on the three viewpoints that an excitatory autapse can induce abnormal dynamical behaviors 59,[62][63][64][65][66][67][68][69] , fast-decay autapses may have similar effects to type II and III excitability 26 , and slow-decay autapses may have effects on neuronal ring patterns different from fast ones 63,64 , the influences of slow-decay excitatory autapses on firing dynamics of type II and III excitability are investigated in the present paper and compared with fast-decay excitatory autapses. Four important results are obtained.…”