Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 176493, 6 pages
http://dx.doi.org/10.1155/2014/176493
Research Article

Global Stability for a Predator-Prey Model with Dispersal among Patches

1Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Harbin 150080, China
2Department of Mathematics, Daqing Normal University, Daqing, Heilongjiang 163712, China

Received 19 January 2014; Accepted 6 February 2014; Published 12 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Yang Gao and Shengqiang Liu. 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. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. D. Murry, Mathematical Biology, vol. 1-2, Springer, New York, NY, USA, 2002.
  3. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. R. Xu, M. A. J. Chaplain, and F. A. Davidson, “Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments,” Nonlinear Analysis: Real World Applications, vol. 5, no. 1, pp. 183–206, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. Zhang and Z. Teng, “Permanence for a delayed periodic predator-prey model with prey dispersal in multi-patches and predator density-independent,” Journal of Mathematical Analysis and Applications, vol. 338, no. 1, pp. 175–193, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Y. Li and Z. Shuai, “Global stability of an epidemic model in a patchy environment,” Canadian Applied Mathematics Quarterly, vol. 17, no. 1, pp. 175–187, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Shu, D. Fan, and J. Wei, “Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission,” Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1581–1592, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. Sun and J. Shi, “Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates,” Applied Mathematics and Computation, vol. 218, no. 2, pp. 280–286, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Wang, J. Zu, X. Liu, G. Huang, and J. Zhang, “Global dynamics of a multi-group epidemic model with general relapse distribution and nonlinear incidence rate,” The Journal of Biological Systems, vol. 20, no. 3, pp. 235–258, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  14. N. Moshtagh, A. Jadbabaie, and K. Daniilidis, “Distributed geodesic control laws for flocking of nonholonomic agents,” in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC '05), pp. 2835–2840, December 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. R. A. Freeman, Y. Peng, and K. M. Lynch, “Distributed estimation and control of swarm formation statistics,” in Proceedings of the American Control Conference, pp. 749–755, June 2006. View at Scopus
  16. Y. Hong, L. Gao, D. Cheng, and J. Hu, “Lyapunov-based approach to multiagent systems with switching jointly connected interconnection,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 943–948, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  17. R. Olfati-Saber and J. S. Shamma, “Consensus filters for sensor networks and distributed sensor fusion,” in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC '05), pp. 6698–6703, December 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. M. T. Hagan, H. B. Demuth, and M. H. Beale, Neural Network Design, China Machine, Beijing, China, 2002.
  19. Z. H. Zhou and C. G. Cao, Neural Network with Applications, Tsinghua University Press, Beijing, China, 2004.
  20. C. Hu, J. Yu, H. Jiang, and Z. Teng, “Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control,” Nonlinearity, vol. 23, no. 10, pp. 2369–2391, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. H. K. Khalil, Nonlinear Systems, Prentice Hall, 3rd edition, 2002.