Dynamics Of A Brusselsator System Under Non-Gaussian Noise Excitation

Noise exists in nature widely.Under the certain nonlinear conditions,noise can play a decisive role in the evolution of the system,and even change the fate of the macroscopic system.In recent years,the steady-state characteristics,transient characteristics and stochastic resonance(SR)of nonlinear systems driven by random noise have become a hot topic.In this paper,the steady-state characteristics,transient characteristics and SR of Brusselator system driven by non Gaussian noise are studied.The main contents and conclusions are as follows.1.The steady-state characteristics and SR of Brusselator system driven by non-Gaussian noise are studied.Firstly,the steady-state characteristics and SR of Brusselator system driven by Lévy noise are analyzed.The stationary probability density(SPD)function and the signal-to-noise ratio(SNR)function of the system are obtained by employing Janicki-weron algorithm and fourth-order Runge-Kutta algorithm.The influence of noise parameters on the SPD and SR of the system is further discussed.The results show that the stability index,symmetry parameter and noise intensity can induce the phase transition of the system,and the larger stability index,symmetric parameter and amplitude are conducive to the occurrence of SR.Secondly,the SR of Brusselator system driven by non-Gaussian noise is mainly discussed.The model is processed by linear transformation method and stochastic normal form.And we obtained the analytical expressions of SNR of Brusselator system driven by non-Gaussian noise and periodic signal.Then the SR of the system is reflected by simulating the SNR of the system.The results show that the smaller correlation time and larger amplitude are beneficial to the occurrence of SR,and it is found that correlation time has the greatest influence on the system,and non Gaussian parameters have the least influence on the system.2.The transient characteristics of Brusselator system driven by non-Gaussian noise are studied.Firstly,the transient characteristics of Brusselator system driven by Lévy noise are discussed.The Janicki-weron algorithm is employed to simulate Lévy noise,and the fourth-order Runge-Kutta algorithm is applied to solve the system equations.The probability density distribution functions of first passage time(FPT)and mean first passage time(MFPT)are obtained.Then the influence of noise parameters on MFPT is discussed.It is indicated that the higher additive noise intensity and skew parameters are beneficial to the formation of products.The influence of stability index on particle transition is different,and the influence mode is related to the intensity of additive noise.Next,the transient characteristics of Brusselator system driven by non-Gaussian noise are studied.The non-Gaussian noise is approximated to Gaussian colored noise by path integral method,and the fourth-order Runge-Kutta algorithm is employed to solve the system equation.The probability density distribution functions of the FPT and the MFPT are also obtained,and the influence of noise parameters on the MFPT of the system is discussed.It is found that the higher additive noise intensity and the lower correlation time are conducive to the formation of products.