ON THE TWO BIFURCATIONS OF A WHITE-NOISE EXCITED HOPF BIFURCATION SYSTEM

The present work is concerned with the behavior of the second bifurcation of a Hopf bifurcation system excited by white-noise. It is found that the intervention of noises induces a drift of the bifurcation point along with the subtantial change in bifurcation type.

Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model

An approximate Fokker-Planck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution （SPD） and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ is in -1 〈λ≤0 and can be the double extrema in 0〈λ〈1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, （x）, versus λ The position and the value of the minimum are controlled by the noise-correlated times.

Intensity Correlation Function and Associated Relaxation Time of a Saturation Laser Model with Correlated Noises

We investigate the intensity correlation function C（s） and its associated relaxation time Tc for a saturation model of single-mode laser with correlated noises. The expressions of O（s） and Tc are derived by means of the projection operator method, and effects of correlations between an additive noise and a multiplicative noise are discussed by numerical calculation. Based on the calculated results, it is found that the correlation strength A between the additive noise and the multiplicative noise can enhance the fluctuation decay of the laser intensity.

Asymptotical p-Moment Stability of Stochastic Impulsive Differential Equations and Its Application in Impulsive Control

In this paper, the asymptotical p-moment stabifity of stochastic impulsive differential equations is studied, and a comparison theory to ensure the asymptotieal p-moment stability for trivial solution of this system is established, from which we can find out whether a stochastic impulsive differential system is stable just from a deterministic comparison system. As an application of this theory, we control the chaos of stochastic Chen system using impulsive method, and a stable region is deduced too. Finally, numerical simulations verify the feasibility of our method.

The stationary solution of a random dynamical model

This paper studies the stationary probability density function（PDF） solution of a nonlinear business cycle model subjected to random shocks of Gaussian white-noise type. The PDF solution is controlled by a Fokker–Planck– Kolmogorov（FPK） equation, and we use exponential polynomial closure（EPC） method to derive an approximate solution for the FPK equation. Numerical results obtained from EPC method, better than those from Gaussian closure method, show good agreement with the probability distribution obtained with Monte Carlo simulation including the tail regions.

p-moment stability of stochastic impulsive differential equations and its application in impulsive control

The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.

WHITE NOISE ESTIMATION FOR DISCRETE-TIME SYSTEMS WITH RANDOM DELAY AND PACKET DROPOUT

This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal input white noise estimator is presented based on the stochastic Kahnan filtering theory. However, tb_e optimal white-noise estimator is timevarying, stochastic, and doesn＇t converge to a steady state in general. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criteria. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.