Effect Of Time Delay On Synchronization And Stochastic Resonance In Small-world Neuronal Network

Synchronization and resonance in neuroscience have significant effects oninformation transmission and processing of neuronal network and have beenincreasing interests and intensively studied in recent years. Synchronization ofneuronal network is a phenomenon that all neurons in network spike consistently orwith a constant time interval. However, stochastic resonance of neuronal network is aphenomenon that a nonlinear dynamic system added a weak signal in noiseenvironment can generate an optimal output signal-to-noise ratio. Clinical evidencesalso suggested that some neurological diseases, such as Parkinson s disease, epilepsy,and trembling can be induced by synchronization of neuronal networks. Thus, it isstudied that the effect of different network parameters, such as the coupling strength,time delay and rewiring probability on synchronization and stochastic resonance ofsmall-world neuronal network based on two-dimensional map model proposed byRulkov in order to provide a theoretical basis of deep understanding of informationtransmission and processing of neuronal network and pathogenic mechanism of theneurological diseasesThe electric excitatory and inhibitory synapses coupling of small world neuronalnetwork on synchronization is discussed respectively and the local and globalsynchronization of small world neuronal network is distinguished in detail. Numericalresults show that synchronization of neuronal activity in small-world network can beeither promoted or destroyed as time delay changing. In particular, the regions ofin-phase synchronization and anti-phase synchronization appear intermittently.However, the effect of the rewiring probability on synchronization is more complex.The rewiring probability has an influence on local synchronization hardly. But thesynchronous regimes of the global network transfer from out-of-phasesynchronization to in-phase synchronization in some appropriate time delay regionswith electrical excitatory and inhibitory synapses as the rewiring probabilityincreasing. This means the neuronal network approaching to a random network caninduce global in-phase synchronization in some appropriate time delay regions withelectrical excitatory and inhibitory synapses. It is shown that irrespective of the pacemaker introduced to one single neuron orall neurons of the network, the phenomenon of stochastic resonance occurs. The timedelay in the coupling process can either enhance or destroy stochastic resonance onsmall-world neuronal networks. In particular, appropriately tuned delays can inducemultiple stochastic resonances, which appear intermittently at integer multiples of theoscillation period of the pacemaker. More importantly, it is found that the small-worldtopology can significantly affect the stochastic resonance on excitable neuronalnetworks. For small time delays, increasing the rewiring probability can largelyenhance the efficiency of pacemaker-driven stochastic resonance. Thus, time delayand the rewiring probability both play key roles in determining the ability of thesmall-world neuronal network to improve stochastic resonance and synchronization.