Dynamics of non-autonomous stochastic Gilpin-Ayala competition model with time-varying delays

Applied Mathematics and Computation

Volumn 219, Issue 12, 2013, Pages 6946-6964

  Jovanović, Miljana ^a   Vasilova, Maja ^a  

^a UNIVERSITY OF NI   (Serbia)

Author keywords

Asymptotic behavior; Extinction; Gilpin Ayala competition model; Non persistence in time average; Time dependent delay; Weak persistence

Indexed keywords

ASYMPTOTIC BEHAVIORS; COMPETITION MODEL; TIME AVERAGES; TIME-DEPENDENT; WEAK PERSISTENCE;

LIGHT EXTINCTION; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 84874044067     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.12.073     Document Type: Article

References (32)

1. A. Lotka Elements of Physical Biology 1924 Williams and Wilkins Baltimore, MD
2. V. Volterra Variazioni e fluttuazioni del numero d'individui in specie d'animali conviventi Mem. Acad. Lincei 2 1926 31 113
3. K. Gopalsamy Persistence in periodic and almost periodic Lotka-Volterra systems J. Math. Biol. 21 1984 145 148
4. M.L. Zeeman Extinction in competitive Lotka-Volterra systems Proc. Am. Math. Soc. 123 1995 87 96
5. J. Qiu, and J. Cao Exponential stability of a competitive Lotka-Volterra system with delays Appl. Math. Comput. 201 2008 819 829
6. M. Liao, X. Tang, and C. Xu Dynamics of a competitive Lotka-Volterra system with three delays Appl. Math. Comput. 217 2011 10024 10034
7. M.E. Gilpin, and F.J. Ayala Global models of growth and competition Proc. Natl. Acad. Sci. USA 70 1973 3590 3593
8. X. Mao, G. Marion, and E. Renshaw Environmental Brownian noise suppresses explosions in population dynamics Stoch. Process. Appl. 97 2002 95 110
9. X. Mao, S. Sabanis, and E. Renshaw Asymptotic behaviour of the stochastic Lotka-Volterra model J. Math. Anal. Appl. 287 2003 141 156
10. N.H. Du, and V.H. Sam Dynamics of a stochastic Lotka-Volterra model perturbed by white noise J. Math. Anal. Appl. 324 2006 82 97
11. C. Zhu, and G. Yin On competitive Lotka-Volterra model in random environments J. Math. Anal. Appl. 357 2009 154 170
12. F. de la Hoz, and F. Vadillo A mean extinction-time estimate for a stochastic Lotka-Volterra predator-prey model Appl. Math. Comput. 219 2012 170 179
13. E. Renshaw Stochastic Population Processes: Analysis, Approximations, Simulations 2011 Oxford University Press
14. B. Lian, and S. Hu Asymptotic behaviour of the stochastic Gilpin-Ayala competition models J. Math. Anal. Appl. 339 2008 419 428
15. B. Lian, and S. Hu Stochastic delay Gilpin-Ayala competition models Stoch. Dyn. 6 2006 561 576
16. A. Bahar, and X. Mao Stochastic delay Lotka-Volterra model J. Math. Anal. Appl. 292 2004 364 380
17. L. Wan, and Q. Zhou Stochastic Lotka-Volterra model with infinite delay Statist. Probab. Lett. 79 2009 698 706
18. Y. Xu, F. Wu, and Y. Tan Stochastic Lotka-Volterra system with infinite delay Comput. Appl. Math. 232 2009 472 480
19. M. Vasilova, and M. Jovanović Dynamics of Gilpin-Ayala competition model with random perturbation Filomat 24 1 2010 101 113
20. M. Vasilova, and M. Jovanović Stochastic Gilpin-Ayala competition model with infinite delay Appl. Math. Comput. 217 2011 4944 4959
21. M. Fan, and K. Wang Global periodic solutions of a generalized n-species Gilpin-Ayala competition model Comput. Math. Appl. 40 2000 1141 1151
22. F. Chen Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala competition model with delays Nonlinear Anal. Real World Appl. 7 2006 1205 1222
23. Y. Xia, M. Han, and Z. Huang Global attractivity of an almost N-species nonlinear ecological competitive model J. Math. Anal. Appl. 337 2008 144 168
24. J. Yan Global positive periodic solutions of periodic n-species competition systems J. Math. Anal. Appl. 356 2009 288 294
25. X. Mao Stochastic Differential Equations and Applications second ed. 2007 Horwood
26. S.C. Gamradt, and L.B. Kats Effect of introduced crayfish and mosquitofish on California newts Conserv. Biol. 10 1996 1155 1162
27. S.L. Plimm, H.L. Jones, and J. Diamond On the risk of extinction Am. Nat. 132 6 1988 757 785
28. T.G. Hallam, and Z.E. Ma Persistence in population models with demographic fluctuations J. Math. Biol. 24 1986 327 399
29. Z.E. Ma, and T.G. Hallam Effects of parameter fluctuations on community survival Math. Biosci. 86 1987 35 49
30. M. Liu, and K. Wang Survival analysis of stochastic single-species population models in polluted environments Ecol. Model. 220 2009 1347 1357
31. M. Liu, and K. Wang Persistence and extinction in stochastic non-autonomous logistic systems J. Math. Anal. Appl. 375 2011 42 57
32. X. Li, and X. Mao Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation Discrete Contin. Dyn. Syst. 24 2 2009 523 545