论文信息 - Stationary probability distributions of some lotka-volterra types of stochastic predation systems

Stationary probability distributions of some lotka-volterra types of stochastic predation systems

This paper provides exact solutions to the stationary probability distributions in some stochastic predation systems. These are derived by solving the Fokker-Planck equations for: (i) a generalized stochastic Lotka-Volterra predator-prey system, and (ii) a generalised stochastic Lotka-Volterra food chain. In all these systems the growth dynamics of all levels of species are subject to stochastic shocks. Since stationary probability distributions provide the most comprehensive characterization of a stochastic system in a steady state, system stability can be analysed accordingly

David W. K. Yeung | D. Yeung | Sally Stewart | Sally Stewart

[1] Jim M Cushing,et al. Two species competition in a periodic environment , 1980 .

[2] A. J. Lotka,et al. Elements of Physical Biology. , 1925, Nature.

[3] D. Yeung. Exact solution for steady–state probability distribution of a simple stochastic lotka–volterra food chain , 1988 .

[4] G. Ladde,et al. Stability and limiting distributions of one and two species stochastic population models , 1984 .

[5] V. Lakshmikantham,et al. Random differential inequalities , 1980 .

[6] A. J. Lotka. Elements of Physical Biology. , 1925, Nature.

[7] S. C. Liu. Solutions of fokker-planck equation with applications in nonlinear random vibration , 1969 .

[8] K. Gopalsamy,et al. Global asymptotic stability in a periodic Lotka-Volterra system , 1985, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[9] Xiao-Qiang Zhao,et al. The qualitative analysis of n-species Lotka-Volterra periodic competition systems , 1991 .

[10] David W. K. Yeung,et al. Optimal management of replenishable resources in a predator-prey system with randomly fluctuating population , 1986 .

[11] T. T. Soong,et al. Random differential equations in science and engineering , 1974 .