Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 637862, 10 pages
http://dx.doi.org/10.1155/2014/637862
Research Article

Analysis of Stochastic Gilpin-Ayala Competition System

1College of Science, Hohai University, Nanjing 210098, China
2School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing 210023, China

Received 4 August 2014; Accepted 4 September 2014; Published 5 November 2014

Academic Editor: Ramachandran Raja

Copyright © 2014 Lei Liu and Quanxin Zhu. 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.

Linked References

  1. M. E. Gilpin and F. G. Ayala, “Global models of growth and competition,” Proceedings of the National Academy of Sciences of the United States of America, vol. 70, pp. 3590–3593, 1973. View at Publisher · View at Google Scholar
  2. D. Jiang and N. Shi, “A note on nonautonomous logistic equation with random perturbation,” Journal of Mathematical Analysis and Applications, vol. 303, no. 1, pp. 164–172, 2005. View at Publisher · View at Google Scholar
  3. D. Jiang, N. Shi, and X. Li, “Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation,” Journal of Mathematical Analysis and Applications, vol. 340, no. 1, pp. 588–597, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. C. Y. Ji, D. Q. Jiang, and N. Z. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. X. Li, A. Gray, D. Jiang, and X. Mao, “Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching,” Journal of Mathematical Analysis and Applications, vol. 376, no. 1, pp. 11–28, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. M. Liu and K. Wang, “Persistence and extinction in stochastic non-autonomous logistic systems,” Journal of Mathematical Analysis and Applications, vol. 375, no. 2, pp. 443–457, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. X. Mao, S. Sabanis, and E. Renshaw, “Asymptotic behaviour of the stochastic Lotka-Volterra model,” Journal of Mathematical Analysis and Applications, vol. 287, no. 1, pp. 141–156, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. C. Zhu and G. Yin, “On hybrid competitive Lotka-Volterra ecosystems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 12, pp. e1370–e1379, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. X. Mao, “Stationary distribution of stochastic population systems,” Systems & Control Letters, vol. 60, no. 6, pp. 398–405, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. D. Jiang, C. Ji, X. Li, and D. O'Regan, “Analysis of autonomous Lotka-Volterra competition systems with random perturbation,” Journal of Mathematical Analysis and Applications, vol. 390, no. 2, pp. 582–595, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. M. Liu and K. Wang, “Stationary distribution, ergodicity and extinction of a stochastic generalized logistic system,” Applied Mathematics Letters, vol. 25, no. 11, pp. 1980–1985, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. H. Liu, X. Li, and Q. Yang, “The ergodic property and positive recurrence of a multi-group Lotka-Volterra mutualistic system with regime switching,” Systems & Control Letters, vol. 62, no. 10, pp. 805–810, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. N. Ikeda Wantanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, The Netherlands, 1981.
  16. R. Z. Hasminskii, Stochastic Stability of Differential Equations, Springer, Berlin, Germany, 2011.
  17. X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College Press, London, UK, 2006.