Lévy Noise-induced Dynamics In The Co Catalytic Oxidation And Perceptual Bistability

All real-world systems operate in a very noisy environment.The fluctuations can interact with the nonlinearities of the system,leading to varieties of behaviors.Over the past few years,the effect of the noise excitation on the nonlinear dynamics has been received increased attention.Most of the studies so far only account for Gaussian noise.However,the noises inherently presented in different nonlinear systems are often characterized by strong“jumps”.Here we replace the Gaussian noise with a more general Lévy noise.The latter exhibits the asymptotic power-law decay and is more appropriate to describe the fluctuations in nature.The influences of Lévy noise in CO catalytic oxidation and in perceptual bistability phenomena are examined numerically.The content of this dissertation is given:(1)The influences of external Lévy noise in CO catalytic oxidation are considered when the perturbation is added to the CO fraction.Numerical evidences are provided to show the effects of Lévy noise on the probability distribution function.When the noise-free system is monostable,noise-induced shift of the steady state can be observed by varying the stability index,the noise intensity or the skewness parameter.When the noise-free system shows a bistable behavior,the number of maxima in the probability distributions can change as functions of and,indicating the stochastic bifurcation.The results give strong evidences for different effects between Lévy noise and Gaussian one.We further show the bifurcation diagrams on different parameter planes.It is confirmed that and could be regarded as relevant control parameter for stochastic bifurcation.(2)The kinetics of CO catalytic oxidation is investigated when an OUL process is superposed on the temperature.The stationary probability distributions are measured as functions of the parameters characterizing the OUL process.It is found that noise-induced transition can occur no matter which noise parameter,or₉),is chosen as the control parameter.We also examine the effect of OUL process on the average CO₂ rate.The results indicate that when the OUL process leads back to the standard OU process,the average reaction rate reaches the minimum.In addition,we plot the bifurcation diagrams on the parameter plane of the molar fraction of CO and the temperature for different values of the parameters of the OUL and find that the size of the bistability region is closely connected with the parameters.(3)The alternations in a model of perceptual bistability are studied under the influence of Lévy noise.We consider the phase transition in terms of the stationary probability densities,in relation to the input strengths.When the input strength of one percept is not equal to the other one,a transition from a monostable to a bimodal distribution is observed due to the increasing skewness parameter.In contrast,no transition occurs by varying the stability index or the noise intensity.When inputs are the same for the two percepts,only the parameter is responsible for the noise-induced transition.We also show the influences of Lévy noise on the mean dominance duration of each percept and the alternation rate.It shows that changing the value of one of the parameters of Lévy noise can change the mean dominance duration of the percepts and their alternation rate.(4)Based on a competitive neural model,the effects of the OUL process in binocular rivalry are analyzed numerically.We first investigate how the OUL process added to the input strength changes the period of oscillations.It is observed that the winner-take-all behavior disappears.All the parameters of the OUL process can change the period of oscillations for the system.We are then interested in the overlapping of the regions where the model's behavior satisfies the experimental constraints on the mean dominance duration and the coefficient of variation of the dominance durations.The results indicate that the change in each of the parameters of the OUL process is capable of changing the overlap regions with different patterns.Finally we examine the effects of the OUL process on the distributions of the perceptual dominance durations.We show the distributions of the perceptual dominance durations for different parameters of the OUL process and fit these distributions with Gamma,Log-normal and Weibull distributions using the Kolmogorov-Smirnov goodness-of-fit test.