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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 125089, 9 pages
Persistence and Nonpersistence of a Food Chain Model with Stochastic Perturbation
1School of Mathematics, Jilin University, Changchun, Jilin 130024, China
2Department of Basic Courses, Air Force Aviation University, Changchun, Jilin 130022, China
3School of Mathematics, Northeast Normal University, Changchun, Jilin 130024, China
Received 3 June 2013; Accepted 21 September 2013
Academic Editor: Mark McKibben
Copyright © 2013 Haihong Li 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.
- B. S. Goh, “Global stability in many species system,” American Naturalist, vol. 111, pp. 135–143, 1997.
- H. I. Freedman, Deterministic Mathematical Models in Population Ecology, vol. 57, Marcel Dekker, New York, NY, USA, 1980.
- Y. Kuang and H. L. Smith, “Global stability for infinite delay Lotka-Volterra type systems,” Journal of Differential Equations, vol. 103, no. 2, pp. 221–246, 1993.
- K. Gopalsamy, “Global asymptotic stability in a periodic Lotka-Volterra system,” Journal of Australian Mathematical Society B, vol. 24, pp. 160–170, 1985.
- T. C. Gard, Introduction to Stochastic Differential Equations, vol. 114, Marcel Dekker, New York, NY, USA, 1988.
- T. C. Gard, “Persistence in stochastic food web models,” Bulletin of Mathematical Biology, vol. 46, no. 3, pp. 357–370, 1984.
- T. C. Gard, “Stability for multispecies population models in random environments,” Nonlinear Analysis. Theory, Methods & Applications, vol. 10, no. 12, pp. 1411–1419, 1986.
- X. Mao, G. Marion, and E. Renshaw, “Environmental Brownian noise suppresses explosions in population dynamics,” Stochastic Processes and Their Applications, vol. 97, no. 1, pp. 95–110, 2002.
- X. Mao, “Delay population dynamics and environmental noise,” Stochastics and Dynamics, vol. 5, no. 2, pp. 149–162, 2005.
- Y. Hu, F. Wu, and C. Huang, “Stochastic Lotka-Volterra models with multiple delays,” Journal of Mathematical Analysis and Applications, vol. 375, no. 1, pp. 42–57, 2011.
- N. I. Wantanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, The Netherlands, 1981.
- C. Ji, D. Jiang, N. Shi, and D. O'Regan, “Existence, uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation,” Mathematical Methods in the Applied Sciences, vol. 30, no. 1, pp. 77–89, 2007.
- C. Zhu and G. Yin, “On competitive Lotka-Volterra model in random environments,” Journal of Mathematical Analysis and Applications, vol. 357, no. 1, pp. 154–170, 2009.
- 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 X. Li, “Qualitative analysis of a stochastic ratio-dependent predator-prey system,” Journal of Computational and Applied Mathematics, vol. 235, no. 5, pp. 1326–1341, 2011.
- R. M. May, Stability and Complexity in Model Ecosystem, Princeton University Press, Princeton, NJ, USA, 2001.
- P. Polansky, “Invariant distributions for multipopulation models in random environments,” Theoretical Population Biology, vol. 16, no. 1, pp. 25–34, 1979.
- M. Barra, D. G. Grosso, A. Gerardi, G. Koch, and F. Marchetti, Some Basic Properties of Stochastic Population Models, Springer, Berlin, Germany, 1979.
- X. R. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, UK, 1997.
- L. S. Chen and J. Chen, Nonlinear Biological Dynamical System, Science Press, Beijing, USA, 1993.
- P. Y. Xia, X. K. Zheng, and D. Q. Jiang, “Persistence and nonpersistence of a nonautonomous stochastic mutualism system,” Abstract and Applied Analysis, vol. 2013, Article ID 256249, 13 pages, 2013.
- C. Y. Ji and D. Q. Jiang, “Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response,” Journal of Mathematical Analysis and Applications, vol. 381, no. 1, pp. 441–453, 2011.
- D. J. Higham, “An algorithmic introduction to numerical simulation of stochastic differential equations,” SIAM Review, vol. 43, no. 3, pp. 525–546, 2001.