Existence, stationary distribution, and extinction of predator-prey system of prey dispersal with stochastic perturbation

Abstract and Applied Analysis

Volumn 2012, Issue , 2012, Pages

  Zu, Li ^a,b   Jiang, Daqing ^a   Jiang, Fuquan ^c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b CHANGCHUN UNIVERSITY   (China)

^c Harbin Finance University   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84868682398     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2012/547152     Document Type: Article

References (23)

1. Kuang Y., Takeuchi Y., Predator-prey dynamics in models of prey dispersal in two-patch environments. Mathematical Biosciences 1994 120 1 77 98 10.1016/0025-5564(94)90038-8 1281745 ZBL0793.92014
2. Li M. Y., Shuai Z., Global-stability problem for coupled systems of differential equations on networks. Journal of Differential Equations 2010 248 1 1 20 10.1016/j.jde.2009.09.003 2557892 ZBL1190.34063
3. Beretta E., Solimano F., Takeuchi Y., Global stability and periodic orbits for two-patch predator-prey diffusion-delay models. Mathematical Biosciences 1987 85 2 153 183 10.1016/0025-5564(87)90051-4 910243 ZBL0634.92017
4. Freedman H. I., Takeuchi Y., Global stability and predator dynamics in a model of prey dispersal in a patchy environment. Nonlinear Analysis. Theory, Methods & Applications 1989 13 8 993 1002 10.1016/0362-546X(89)90026-6 1009083 ZBL0685.92018
5. Padrón V., Trevisan M. C., Environmentally induced dispersal under heterogeneous logistic growth. Mathematical Biosciences 2006 199 2 160 174 10.1016/j.mbs.2005.11.004 2211623 ZBL1086.92054 (Pubitemid 43197778)
6. Mao X., Yuan C., Zou J., Stochastic differential delay equations of population dynamics. Journal of Mathematical Analysis and Applications 2005 304 1 296 320 10.1016/j.jmaa.2004.09.027 2124664 ZBL1062.92055 (Pubitemid 40317335)
7. Teng Z., Chen L., Permanence and extinction of periodic predator-prey systems in a patchy environment with delay. Nonlinear Analysis. Real World Applications 2003 4 2 335 364 10.1016/S1468-1218(02)00026-3 1942689 ZBL1018.92033
8. Wendi W., Zhien M., Asymptotic behavior of a predator-prey system with diffusion and delays. Journal of Mathematical Analysis and Applications 1997 206 1 191 204 10.1006/jmaa.1997.5212 1429287 ZBL0872.92019 (Pubitemid 127175681)
9. Xu R., Chen L., Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment. Computers & Mathematics with Applications 2000 40 4-5 577 588 10.1016/S0898-1221(00)00181-4 1772656 ZBL0949.92028
10. Cui J., The effect of dispersal on permanence in a predator-prey population growth model. Computers & Mathematics with Applications 2002 44 8-9 1085 1097 10.1016/S0898-1221(02)00217-1 1937569 ZBL1032.92032 (Pubitemid 35250560)
11. Zhang L., Teng Z., Boundedness and permanence in a class of periodic time-dependent predator-prey system with prey dispersal and predator density-independence. Chaos, Solitons and Fractals 2008 36 3 729 739 10.1016/j.chaos.2006.07.003 2381707 (Pubitemid 350297941)
12. Lu Z. Y., Takeuchi Y., Global asymptotic behavior in single-species discrete diffusion systems. Journal of Mathematical Biology 1993 32 1 67 77 10.1007/BF00160375 1256831 ZBL0799.92014
13. Ji C., Jiang D., Shi N., Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation. Journal of Mathematical Analysis and Applications 2009 359 2 482 498 10.1016/j.jmaa.2009.05.039 2546763 ZBL1190.34064
14. Ji C., Jiang D., Shi N., 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 2011 377 1 435 440 10.1016/j.jmaa.2010.11.008 2754843 ZBL1216.34040
15. Cai G., Lin Y., Stochastic analysis of predator-prey type ecosystems. Ecological Complexity 2007 4 4 242 249 10.1016/j.ecocom.2007.06.011 (Pubitemid 47419445)
16. Li X., Jiang D., Mao X., Population dynamical behavior of Lotka-Volterra system under regime switching. Journal of Computational and Applied Mathematics 2009 232 2 427 448 10.1016/j.cam.2009.06.021 2555412 ZBL1173.60020
17. Mao X., Stochastic Differential Equations and Applications 1997 New York, NY, USA Horwood
18. Li X., Mao X., Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete and Continuous Dynamical Systems A 2009 24 2 523 545 10.3934/dcds.2009.24.523 2486589 ZBL1161.92048
19. Ji C., Jiang D., Liu H., Existence, uniqueness and ergodicity of positive solution of mutualism system with stochastic perturbation. Mathematical Problems in Engineering 2010 10 1155 1172
20. Mao X., Yuan C., Stochastic Differential Equations with Markovian Switching 2006 London, UK Imperial College Press 2256095
21. Higham D. J., An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Review 2001 43 3 525 546 10.1137/S0036144500378302 1872387 ZBL0979.65007 (Pubitemid 32991214)
22. Guo H., Li M. Y., Shuai Z., A graph-theoretic approach to the method of global Lyapunov functions. Proceedings of the American Mathematical Society 2008 136 8 2793 2802 10.1090/S0002-9939-08-09341-6 2399043 ZBL1155.34028
23. Has'minskii R. Z., Stochastic Stability of Differential Equations 1980 Alphen aan den Rijn, The Netherlands Sijthoff Noordhoff 600653