The Phenomenon Of Multiple Stochastic Resonance In Small-World Neuronal Network

Noise is unavoidable in nonlinear system and it has been shown that many biological systems are considered to be stochastic rather than deterministic.It has been proved that subthreshold signal cannot trigger a spike without the existence of noise in neuronal system,thus stochastic resonance can be a mechanism for the efficiency of signal detection in brain.Moreover,there exist more than one optimal noise intensity that enhance the signal detection ability which called multiple stochastic resonance.Li et al have found that multiple stochastic resonance are appearing upon the small-world neuronal network constructed by FitzHugh-Nagumo(FHN)neurons.Based on the above mentioned results,multiple stochastic resonance induced by coupling strength are investigated.When the noise intensity is fixed in an appropriate level,coupling strength can induce the phenomena of multiple stochastic resonance.The firing pattern and its statistic feature of pattern are investigated in this paper.We find out that there is a transition from firing twice in one period to firing once in one period with increasing of coupling strength.Moreover,the effects of network topology under different coupling strength on signal detection ability are also investigated.We obtain that when system are weakly coupled,network properties have little influence on signal detection ability;while at middle-level of coupling strength,the ability of signal detection greatly dependents on the characteristic length of neuronal network;at last when system is strongly coupled there exist optimal characteristic path length of network that enhancing the ability of signal detection.Moreover,the combined effects of time delay and noise on the ability of such small-world neuronal networks to detect subthreshold signal are investigated as well.With the numerical simulation results,three important information can be obtained.Firstly,when noise intensity takes optimal values,the ability of neuronal network to detect the subthreshold signal could be either maintained at high level as delay-free case or decreased by time delay;Secondly,when noise intensity is not optimal in the absence of time delay,time delay could assist noise to detect the subthreshold signal;Finally,when noise reaches a certain level,the detecting ability of the neuronal network could be optimized not only at multiples of the period of the subthreshold signal but also at some small values of time delay.Stochastic resonance has been found in a wide range of neuronal systems.For example,in sharks' multi-modal sensory cell,subthreshold oscillations cannot trigger the action potential and transmit the information without assistance of noise.It is well known that EEG is a common technology for recording neuronal activity.The mechanism of EEG is that certain noise can enhance synchronization of neuronal system,then the neural oscillation can be easily detected.So the usage of noise is important for neuronal systems.Moreover,time delay,coupling strength and network topology are of vital importance in signal processing in neuronal system.Therefore,we hope the obtained results in this paper could give some enlightenment in neuronal information processing of neuronal systems.