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Periodic solutions of a two-species ratio-dependent predator-prey system with time delay in a two-patch environment

Published online by Cambridge University Press:  17 February 2009

Zhengqiu Zhang  and
Zhicheng Wang
Zhengqiu Zhang
Affiliation:
Department of Applied Mathematics, Hunan University, Changsha, Hunan 410082, P. R. China; e-mail: [email protected].
Zhicheng Wang
Affiliation:
Department of Applied Mathematics, Hunan University, Changsha, Hunan 410082, P. R. China; e-mail: [email protected].
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Abstract

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By using the continuation theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution of a predator-prey diffusion system.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 2 , October 2003 , pp. 233 - 244
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Freedman, H. I. and Wu, J., “Periodic solutions of single-species models with periodic delay”, SIAM J. Math. Anal. 23 (1992) 689–701.Google Scholar
[2]Gaines, R. E. and Mawhin, J. L., Coincidence degree and non-linear differential equations (Springer, Berlin, 1977).CrossRefGoogle Scholar
[3]Kuang, Y., Delay differential equations with applications in population dynamics (Academic Press, New York, 1993).Google Scholar
[4]Xu, R. and Chen, L. S., “Persistence and stability for two-species ration-dependent predator-prey system with time delay in a two-patch environment”, Comput. Math. Applic. 40 (2000) 577–588.Google Scholar