The Effects Of Partial Time Delay On Stochastic Resonance And Synchronization In Small World Neuronal Networks

In recent years,the study of stochastic resonance in neuroscience has been paid much attention by many scholars.It is proved that the resonance behaviors have an important influences on the propagation and detection of signals and synchronization is correlated with brain diseases,for example,parkinsons disease,schizophrenia,autism and so on.Time delay plays an important roles in the neural networks.However,the study shows that the transmission of information between some neurons is instantaneous or time-delay is negligible in real neuronal systems.In addition,synapses are mainly consisted by chemical synapses and electrical synapses,and each synapse can be divided into two coupling ways:excitatory coupling and inhibitory coupling.Clinical experiments show that there are differences about the coupled mode of neurons in different regions of the brain.In this paper,the Rulkov map is used as the node model of the network,and the small world network is constructed by the electrical synapse and the mixed synapse.Then,discussing the effects of some parameters,such as partial time delay,noise and coupling strength on the stochastic resonance,and giving the explanation of the mechanism.In the WS and NW small world neuronal networks which only coupled by excitatory electrical synapses,we found that,with the change of time delay probability,partial time delay both can induce the stochastic multi-resonance in two different networks.Especially,when the probability of time delay is less than 20%,a significant phenomenon of stochastic multiple resonance can be induced by partial time delay,and the time delay spans corresponding to the optimal response amplitude is much wider.However,when the probability of time delay is larger,the optimal response amplitude is only near the integer times of time delay to the subthreshold periodic stimulus.Moreover,in the NW small world networks,we also found that partial time delay can induce more frequently stochastic multi-resonance when the probability of partial delay is between 20%and 50%.Furthermore,in the hybrid synapses neuronal networks,the proportion of excitatory synapse to inhibitory ones,partial time delay and noise intensity affect mutually to result in the differences of stochastic resonance.In a network dominated by inhibitory synapses,there is hardly producing the stochastic resonance.It also proved that the relationship between the optimum noise intensity and the proportion of chemical synapses is incremental progressively.Particularly,In a chemically coupled hybrid synaptic network,when the ratio of excitatory synapse to inhibitory synapse is approximately 4:1,noise can induce resonance behaviors.On the basis of this proportion,we introduce the partial time delay,the results revealed that partial time delay can induce the stochastic multi-resonance.Moreover,when setting the time delay being the integer multiple of the system's inherent period,the greater the time delay is,the wider the region of the noise corresponding to the best resonance is and time delay edge is easier to spur noise and delay to induce resonance behaviors.In the E-I mixed synaptic network with excitatory synapses and inhibiting synapses to 4:1,we studied the effect of partial delay on the synchronous transition behavior.The results show that the synchronization behavior of the system is significant when the time delay ratio is small.The main reason is that in the excitatory synapse networks,the synchronization behavior induced by time delay occurs near the even number of half of the natural oscillation period,while in the inhibitory synapse networks,the synchronization behavior induced by time delay occurs near the odd number of half of the natural oscillation period.Hence,with the difference of the proportion of time delay in the inhibitory chemical synapse and the excitatory chemical synapse,partial time delay can induce more complex synchronous transition behavior.In addition,when the ratio of the delay side is the larger,the synchronous transition is robust to the rewiring probability,and the time-delay induced synchronization occurs at the integer number of the natural period.We hope that this article can provide a theoretical basis for the transmission and detection of signals and physiological diseases,so that we can have the essential understanding of the complex mechanism of neural activity in neural networks.