Dynamical Characteristics Of An Asymmetric Bistable System Excited By Lévy Noise And Bounded Nois

Noise is common in nature.In many practical problems,such as physical system,chemical system,biological system and ecosystem,it is inevitable to be disturbed by external noise.Therefore,investigating the impact of noise on system dynamic behavior has become one of the important contents of dynamic development.In this thesis,the transient characteristics and dynamic complexity of asymmetric bistable systems excited by non-Gaussian noise are studied.The main contents and conclusions are as follows:1.The transient characteristics of asymmetric bistable system excited by nonGaussian noise are studied.First of all,the transient characteristics of underdamped asymmetric bistable systems excited by Lévy noise are discussed.The Janicki-weron algorithm is used to generate Lévy noise,and the probability density and average first transit time of the system are simulated by the fourth-order Runge-Kutta algorithm,and then the steady-state analysis is further carried out through its function image.Through numerical simulation,it can be found that the influence of the stability coefficient α,the symmetry parameter β,the asymmetric parameter r of the potential well and the damping coefficient of the system γ on first passage time and mean first passage time in two different directions is different.In addition,we also find that the Lévy noise induced system has noise enhanced stability.Next,the transient characteristics of asymmetric bistable systems excited by correlated bounded noise are studied.The correlated bounded noise is decoupled and transformed in a certain way,and the Euler algorithm is used to numerically solve the system equation.Similarly,the probability density distribution functions of first passage time and mean first passage time are obtained.It is found that different parameters have different effects on the passage time,and the correlated bounded noise also induces the noise enhanced stability of the system.2.The dynamic complexity of asymmetric bistable systems excited by Gaussian white noise and Lévy noise is studied by using statistical complexity and standard Shannon entropy.Considering the asymmetry of the system potential function,the numerical simulation is used to count the total residence time interval of the system and the residence time interval of the left and right potential wells,and the probability distribution function of the residence time interval sequence is constructed by BandtPompe algorithm.Then 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.On this basis,the effects of stability coefficient,symmetric parameters,asymmetric parameters of potential well,additive noise,multiplicative noise and periodic signal on the dynamic complexity of the system are discussed.The results show that when these factors change,the total statistical complexity and standard Shannon entropy of the system are significantly different from those in a single potential well,reflecting the difference of its dynamic complexity.Among them,the total statistical complexity of the images shows a monotonic decreasing trend until it tends to 0,indicating that the complexity of the system is gradually weakened;the image of the total standard Shannon entropy shows a monotonic increasing trend until it tends to 1,indicating that the motion state of the system becomes more and more disordered.In short,the overall complexity of the system will gradually weaken with the increase of the intensity of additive Lévy noise.