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...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.展开更多
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 dist...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.展开更多
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–P...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.展开更多
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 diff...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.展开更多
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No 10275025, and the Key Project of Education Bureau of Hubei Province under Grant No Z200612001.
文摘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.
基金supported by the National Natural Science Foundation of China(11302157)Fundamental Research Funds for the Central Universities(K5051370008)Chinese-Serbian Science&Technology Cooperation(2-14)
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No. 10772046)
文摘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.
