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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 547152, 24 pages
Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation
1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Science, Changchun University, Changchun 130022, China
3Department of Foundation, Harbin Finance University, Harbin 150030, China
Received 24 July 2012; Accepted 13 September 2012
Academic Editor: Yonghui Xia
Copyright © 2012 Li Zu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Y. Kuang and Y. Takeuchi, “Predator-prey dynamics in models of prey dispersal in two-patch environments,” Mathematical Biosciences, vol. 120, no. 1, pp. 77–98, 1994.
- M. Y. Li and Z. Shuai, “Global-stability problem for coupled systems of differential equations on networks,” Journal of Differential Equations, vol. 248, no. 1, pp. 1–20, 2010.
- E. Beretta, F. Solimano, and Y. Takeuchi, “Global stability and periodic orbits for two-patch predator-prey diffusion-delay models,” Mathematical Biosciences, vol. 85, no. 2, pp. 153–183, 1987.
- H. I. Freedman and Y. Takeuchi, “Global stability and predator dynamics in a model of prey dispersal in a patchy environment,” Nonlinear Analysis. Theory, Methods & Applications, vol. 13, no. 8, pp. 993–1002, 1989.
- V. Padrón and M. C. Trevisan, “Environmentally induced dispersal under heterogeneous logistic growth,” Mathematical Biosciences, vol. 199, no. 2, pp. 160–174, 2006.
- X. Mao, C. Yuan, and J. Zou, “Stochastic differential delay equations of population dynamics,” Journal of Mathematical Analysis and Applications, vol. 304, no. 1, pp. 296–320, 2005.
- Z. Teng and L. Chen, “Permanence and extinction of periodic predator-prey systems in a patchy environment with delay,” Nonlinear Analysis. Real World Applications, vol. 4, no. 2, pp. 335–364, 2003.
- W. Wendi and M. Zhien, “Asymptotic behavior of a predator-prey system with diffusion and delays,” Journal of Mathematical Analysis and Applications, vol. 206, no. 1, pp. 191–204, 1997.
- R. Xu and L. Chen, “Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment,” Computers & Mathematics with Applications, vol. 40, no. 4-5, pp. 577–588, 2000.
- J. Cui, “The effect of dispersal on permanence in a predator-prey population growth model,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1085–1097, 2002.
- L. Zhang and Z. Teng, “Boundedness and permanence in a class of periodic time-dependent predator-prey system with prey dispersal and predator density-independence,” Chaos, Solitons and Fractals, vol. 36, no. 3, pp. 729–739, 2008.
- Z. Y. Lu and Y. Takeuchi, “Global asymptotic behavior in single-species discrete diffusion systems,” Journal of Mathematical Biology, vol. 32, no. 1, pp. 67–77, 1993.
- C. Ji, D. Jiang, and N. Shi, “Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation,” Journal of Mathematical Analysis and Applications, vol. 359, no. 2, pp. 482–498, 2009.
- C. Ji, D. Jiang, and N. Shi, “A note on a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation,” Journal of Mathematical Analysis and Applications, vol. 377, no. 1, pp. 435–440, 2011.
- G. Cai and Y. Lin, “Stochastic analysis of predator-prey type ecosystems,” Ecological Complexity, vol. 4, no. 4, pp. 242–249, 2007.
- X. Li, D. Jiang, and X. Mao, “Population dynamical behavior of Lotka-Volterra system under regime switching,” Journal of Computational and Applied Mathematics, vol. 232, no. 2, pp. 427–448, 2009.
- X. Mao, Stochastic Differential Equations and Applications, Horwood, New York, NY, USA, 1997.
- X. Li and X. Mao, “Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation,” Discrete and Continuous Dynamical Systems A, vol. 24, no. 2, pp. 523–545, 2009.
- C. Ji, D. Jiang, and H. Liu, “Existence, uniqueness and ergodicity of positive solution of mutualism system with stochastic perturbation,” Mathematical Problems in Engineering, vol. 10, pp. 1155–1172, 2010.
- X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College Press, London, UK, 2006.
- D. J. Higham, “An algorithmic introduction to numerical simulation of stochastic differential equations,” SIAM Review, vol. 43, no. 3, pp. 525–546, 2001.
- H. Guo, M. Y. Li, and Z. Shuai, “A graph-theoretic approach to the method of global Lyapunov functions,” Proceedings of the American Mathematical Society, vol. 136, no. 8, pp. 2793–2802, 2008.
- R. Z. Has'minskii, Stochastic Stability of Differential Equations, Sijthoff Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.