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Discrete Dynamics in Nature and Society
Volume 2008, Article ID 706154, 13 pages
http://dx.doi.org/10.1155/2008/706154
Research Article

Almost Periodic Solution of a Diffusive Mixed System with Time Delay and Type III Functional Response

Department of Mathematics and Computer Science, Guangxi Qinzhou University, Qinzhou, Guangxi 535000, China

Received 21 February 2008; Accepted 2 June 2008

Academic Editor: Manuel De La Sen

Copyright © 2008 Qiong 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. S. A. Levin, “Dispersion and population interaction,” The American Naturalist, vol. 108, no. 960, pp. 207–228, 1974. View at Publisher · View at Google Scholar
  2. k. kishimoto, “Coexistence of any number of species in the Lotka-Volterra competitive system over two-patches,” Theoretical Population Biology, vol. 38, no. 2, pp. 149–194, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Y. Takeuchi, “Conflict between the need to forage and the need to avoid competition: persistence of two-species model,” Mathematical Biosciences, vol. 99, no. 2, pp. 181–194, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. M. Cushing, “Periodic time-dependent predator-prey systems,” SIAM Journal on Applied Mathematics, vol. 32, no. 1, pp. 82–95, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. Krukonis and W. M. Schaffer, “Population cycles in mammals and birds: does periodicity scale with body size?” Journal of Theoretical Biology, vol. 148, no. 4, pp. 469–493, 1991. View at Publisher · View at Google Scholar
  6. H.-F. Huo and W.-T. Li, “Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model,” Discrete Dynamics in Nature and Society, vol. 2005, no. 2, pp. 135–144, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. K. Liu and L. Chen, “On a periodic time-dependent model of population dynamics with stage structure and impulsive effects,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 389727, 15 pages, 2008. View at Publisher · View at Google Scholar
  8. J. Cui and L. S. Chen, “The effect of diffusion on the time varying logistic population growth,” Computers & Mathematics with Applications, vol. 36, no. 3, pp. 1–9, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. Y. Song and L. S. Chen, “Conditions for global attractivity of n-patches predator-prey dispersion-delay models,” Journal of Mathematical Analysis and Applications, vol. 253, no. 1, pp. 1–15, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z. D. Teng and L. S. Chen, “Positive periodic solutions of periodic Kolmogorov type systems with delays,” Acta Mathematicae Applicatae Sinica, vol. 22, no. 3, pp. 446–456, 1999 (Chinese). View at Google Scholar · View at MathSciNet
  11. Z. Ma, G. Cui, and W. Wang, “Persistence and extinction of a population in a polluted environment,” Mathematical Biosciences, vol. 101, no. 1, pp. 75–97, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Tang and L. S. Chen, “Chaos in functional response host-parasitoid ecosystem models,” Chaos, Solitons & Fractals, vol. 13, no. 4, pp. 875–884, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. F. Wei and K. Wang, “Uniform persistence of asymptotically periodic multispecies competition predator-prey systems with Holling III type functional response,” Applied Mathematics and Computation, vol. 170, no. 2, pp. 994–998, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. K. Hale, Theory of Functional Differential Equations, vol. 3, Springer, New York, NY, USA, 2nd edition, 1977. View at Zentralblatt MATH
  15. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993. View at Zentralblatt MATH · View at MathSciNet
  16. R. Yuan, “Existence of almost periodic solution of functional-differential equations,” Annals of Differential Equations, vol. 7, no. 2, pp. 234–242, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. R. Yuan, “Existence of almost periodic solutions of neutral functional-differential equations via Liapunov-Razumikhin function,” Zeitschrift für Angewandte Mathematik und Physik, vol. 49, no. 1, pp. 113–136, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet