Dynamics Of The FHN Neuron System Under Random Noise Excitation

Stochastic dynamics studies various stochastic dynamical processes and phenomenon in nature,engineering and society using probability and statistics.In the early stage of stochastic dynamics studies is mainly focused on linear stochastic system.However,scholars found that the nonlinear system are included in many practical problems with the deepening of the research.Therefore,we must consider the influence of nonlinear factors on the system movement.At present,the dynamic problems of nonlinear system driven by random force has received the wide concern by scientists in various fields.In this paper,we studied the instability and stability probability density,the mean first-passage time,stochastic resonance in FitzHugh-Nagumo(FHN)neural system driven by random noise.Research methods and conclusions are as follows:We study the steady-state and unsteady-state in FitzHugh-Nagumo(FHN)neural system driven by random noises.Firstly,we studied the instability probability density evolution of the FitzHugh-Nagumo(FHN)neural system which driven by Gaussian colored noise and white noise.The analytical expression of the instability probability density function is derived by applying(?)expansion theory of green function and eigenvalue theory.Further,the effect of noise intensity and correlation time on the instability probability density function were analyzed.The results show that neuron system in a stable state mainly affected by correlation time r.Then,We study the steady-state problems of FitzHugh-Nagumo(FHN)neural system driven by correlated noises.The analytical expression of the steady-state probability density function(SPD)is derived by applying the path integral approach and unified colored noise approximation.The validity of the approximate method was verified and the theoretical results derived from the approximate method highly consistent with the results of numerical simulation.It illustrates that the effectiveness of the approximate method.Next,the effect of parameters of the noise on the instability probability density function were analyzed,we find the noise correlation time τ,additive noise intensity Q can induce the non-equilibrium phase transition,but multiplicative noise intensity D,the cross-correlation strength λ and the non-Gaussian noise deviation parameter q can not induce the transition.We study the mean first-passage time and stochastic resonance in FitzHugh-Nagumo(FHN)neural system driven by correlated noises.Firstly,we investigated the mean first-passage time(MFPT)in FitzHugh-Nagumo(FHN)neural model driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise.The expressions of the MFPT in two directions was derived by applying the definition and the steepest-descent approximation.We found that the multiplicative noise intensity D,the cross-correlation strength λ and the non-Gaussian noise deviation parameter q,it is conducive to switch of the resting state to excited state in neural system.Meanwhile,the additive noise intensity Q and noise correlation time τ can produce adverse effect to transition of the resting state to excited state in neural system.Then,the phenomenon of stochastic resonance in FitzHugh-Nagumo(FHN)neural system driven by correlated non-Gaussian noise and Gaussian white noise is investigated.The analytical expression of the stationary probability distribution is derived by using the path integral approach and the unified colored noise approximation.Further,we obtain the expression of signal-to-noise ratio(SNR)by applying the theory of two-state model.The results show that the phenomena of stochastic resonance and multiple stochastic resonance appear in FHN neural system under different values of additive noise intensity Q,cross-correlation strength λ and the non-Gaussian noise deviation parameter q.