Dynamic Characteristics Of FHN Neuron System Under Excitation Of Gaussian Noise And Lévy Noise

Differential equations and dynamical systems are important theory to study the laws of movement and evolution of things in nature,engineering technology and society.In recent years,the dynamic behavior of nonlinear systems driven by noise has attracted extensive attention.In this paper,the steady-state characteristics,transient characteristics,stochastic resonance and dynamic complexity of FHN neural system driven by Lévy noise and Gaussian noise are studied.The main contents and conclusions are as follows.1.The steady-state and transient characteristics of FHN neuron system driven by Gaussian noise and Lévy noise are discussed.First of all,the steady-state characteristics of two-dimensional FHN neuron system driven by Lévy noise are studied.The steady-state probability density function of the equation is simulated by Janicki-Weron algorithm and fourth-order Runge-Kutta algorithm.The influence of noise parameters and system parameters on the steady-state probability density of the system and the conversion relationship between the excited state and the resting state of the neurons are further analyzed.It is found that both the stability index and the skew parameter can cause the phase transition of the system.Secondly,the transient characteristics of the simplified FHN neural system driven by Gaussian white noise and Lévy noise are studied.The first passage time is calculated by numerical method,and the probability density function and the mean first passage time are obtained.It is found that the influence of different parameters on the time is very different,and the noise induced stability and resonance activation are produced owing to the Lévy noise.2.The stochastic resonance(SR)of FHN neuron system driven by Gaussian noise and Lévy noise is discussed.Firstly,the stochastic resonance of two-dimensional FHN neuron system driven by Lévy noise is studied,and the influence of different parameters on the phenomenon of stochastic resonance is analyzed by simulating the signal-to-noise ratio(SNR).It is found that larger stability index,skew parameter,noise intensity,threshold value,system parameter b and larger ? are beneficial to the occurrence of SR.Secondly,the SR of the simplified FHN neural system driven by Gaussian white noise and Lévy noise is studied.It isfound that a larger stability index and skew parameter,smaller amplitude and ? can improve the SNR of the system,and a are more conducive to the observation of stochastic resonance.3.Based on the method of statistical complexity,the dynamic complexity of FHN neural system driven by Gaussian noise and Lévy noise is discussed.Firstly,the dynamic complexity of the simplified FHN neuron system driven by Gaussian white noise and Lévy noise is studied.The continuous residence time interval of the system and the continuous residence time interval of the left and right potential wells are counted respectively by numerical method.The probability distribution functions of the three residence time interval sequences are constructed by Bandt-Pompe algorithm,the statistical complexity and normalized Shannon entropy of the total,the left potential well and the right potential well of the system are calculated respectively.It is found that Gaussian white noise and Lévy noise have different effects on the complexity of the system.Secondly,the dynamics complexity of the simplified FHN neural system driven by correlated noises and periodic signal is studied.It is found that the total complexity of the system is different from that of a single potential well due to the asymmetry of the system.