A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original s...A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of It6 stochastic differential equations. The It6 formula is then carried out to obtain the It6 stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged It6 stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation.展开更多
The local existence and uniqueness of the solutions to backward stochastic differential equations（BSDEs, in short） driven by both fractional Brownian motions with Hurst parameter H ∈ （1/2, 1） and the underlying s...The local existence and uniqueness of the solutions to backward stochastic differential equations（BSDEs, in short） driven by both fractional Brownian motions with Hurst parameter H ∈ （1/2, 1） and the underlying standard Brownian motions are studied. The generalization of the It6 formula involving the fractional and standard Brownian motions is provided. By theory of Malliavin calculus and contraction mapping principle, the local existence and uniqueness of the solutions to BSDEs driven by both fractional Brownian motions and the underlying standard Brownian motions are obtained.展开更多
In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial...In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11172233,10932009,61171155Natural Science Foundation of Shannxi Province under Grant No.2012JM8010the Doctorate Foundation of Northwestern Polytechnical University under Grant No.CX201215
文摘A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of It6 stochastic differential equations. The It6 formula is then carried out to obtain the It6 stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged It6 stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation.
基金supported by NSFC grant(11371169)China Automobile Industry Innovation and Development Joint Fund(U1564213)
文摘The local existence and uniqueness of the solutions to backward stochastic differential equations（BSDEs, in short） driven by both fractional Brownian motions with Hurst parameter H ∈ （1/2, 1） and the underlying standard Brownian motions are studied. The generalization of the It6 formula involving the fractional and standard Brownian motions is provided. By theory of Malliavin calculus and contraction mapping principle, the local existence and uniqueness of the solutions to BSDEs driven by both fractional Brownian motions and the underlying standard Brownian motions are obtained.
基金Acknowledgments The authors thank the editor and referees for their valuable comments and suggestions. This work is supported by the National Basic Research Program of China （2010CB732501） and the National Natural Science Foundation of China （61273015）, the NSFC Tianyuan Foundation （Grant No. 11226256） and the Zhejiang Provincial Natural Science Foundation of China （Grant No. LY13A010010）, Zhejiang Provincial Natural Science Foundation of China LQ13A010023）.
文摘In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.
