The pth moment Lyapunov exponent of a two-codimension bifurcation system excited parametrically by a real noise is investigated.By a linear stochastic transformation,the differential operator of the system is obtained.In order to evaluate the asymptotic expansion of the moment Lyapunov exponent,via a perturbation method,a ralevant eigenvalue problem is obtained.The eigenvalue problem is then solved by a Fourier cosine series expansion,and an infinite matrix is thus obtained,whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent.Finally,the convergence of procedure is numerically illustrated,and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed.
We investigate the stochastic resonance(SR) phenomenon induced by the periodic signal in a metapopulation system with colored noises. The analytical expression of signal-to-noise is derived in the adiabatic limit. By numerical calculation, the effects of the addictive noise intensity, the multiplicative noise intensity and two noise self-correlation times on SNR are respectively discussed. It shows that:(i) in the case that the addictive noise intensity M takes a small value, a SR phenomenon for the curve of SNR appears; however, when M takes a large value, SNR turns into a monotonic function on the multiplicative noise intensity Q.(ii) The resonance peaks in the plots of the multiplicative noise intensity Q versus its self-correlation time τ1 and the addictive noise intensity M versus its self-correlation time τ2 translate in parallel. Meanwhile, a parallel translation also appears in the plots of τ1 versus Q and τ2 versus M.(iii) The interactive effects between self-correlation times τ1 and τ2 are opposite.
This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.
In the present paper,the moment Lyapunov exponent of a codimensional two-bifurcation system is evaluted,which is on a three-dimensional central manifold and subjected to a parametric excitation by the bounded noise.Based on the theory of random dynamics,the eigenvalue problem governing the moment Lyapunov exponent is established.With a singular perturbation method,the explicit asymptotic expressions and numerical results of the second-order weak noise expansions of the moment Lyapunov are obtained in two cases.Then,the effects of the bounded noise and the parameters of the system on the moment Lyapunov exponent and the stability index are investigated.It is found that the stochastic stability of the system can be strengthened by the bounded noise.
