Research On Dynamic Characteristics Of Segmented Systems Under Random Noise Excitation

Noise is widespread in nature,and it usually produces random interference to useful signals or information.It reflects the role of micro-movement on the evolution of macro-variables in a disorderly manner.In general,noise is considered to be a negative and harmful interference.However,by studying the effect of noise on the nonlinear system,it is found that a weak noise not only plays a decisive role in the evolution of the system,but also can induce the system to produce many new phenomena.In practice,piecewise systems are ubiquitous.Piecewise system dynamics are used in the physical,chemical and biological fields widely.For many experimental systems,the models are based on piecewise system.Such as,electronic circuits,controllers and superconducting devices etc.Therefore,it is necessary to study the piecewise system driven by Gaussian noise.In this paper,we mainly study the non-equilibrium phase transition,noise-induced escape problem and the phenomenon of stochastic resonance in the piecewise system driven by Gaussian noise and non-Gaussian noise.Research methods and conclusions are as follows:We study the steady-state problems of a bistable sawtooth potential driven by correlated noises and a piecewise nonlinear model driven by Gaussian noise.Firstly,applying the path integral approach,the unified colored noise approximation,the analytical expression of the steady-state probability density function(SPD)is derived.Then the change regulation of the SPD is analyzed with the change of the strength and relevance of multiplicative noise and additive noise.Observing the new nonlinear phenomena of the system,we obtain the transition can be induced by the cross-correlation strength between noises,the multiplicative noise intensity and the additive noise intensity.And the effect of the multiplicative noise intensity on SPD is the same as that of the additive noise intensity.Moreover,we also find the correlation time of the Gaussian noise can not induce the transition.We study the mean first-passage time(MFPT)in a piecewise nonlinear model driven by non-Gaussian noise.By using the path integral method,the unified colored noise approximation and the steepest-descent approximation method,the expression of the MFPT is derived.Numerical computation results show that,increasing the intensity of non-Gaussian noise leads to the appearance of a one-peak structure in the MFPT.However,the MFPT of the system decreases with the increase of the additive white noise intensity.This shows that MFPT corresponding to the non-Gaussian noise and Gaussian white noise exhibits very different behavior.The phenomenon of stochastic resonance(SR)in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and a additive Gaussian white noise is investigated.Applying the path integral approach,the unified colored noise approximation and the two-state model theory,the analytical expression of the signal-to-noise ratio(SNR)is derived.It is found that conventional stochastic resonance exists in this system.From numerical computations we obtain that:(?)As a function of the non-Gaussian noise intensity,the SNR is increased when the non-Gaussian noise deviation parameter is increased.(?)As a function of the Gaussian noise intensity,the SNR is decreased when the non-Gaussian noise deviation parameter is increased.This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system.