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Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion

Published online by Cambridge University Press:  13 January 2004

Peter Y. H. Pang  and
Mingxin Wang
Peter Y. H. Pang
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Republic of Singapore 117543. E-mail: matpyh@nus.edu.sg
Mingxin Wang
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210018, People's Republic of China. E-mail: mxwang@seu.edu.cn
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Abstract

This paper deals with non-constant positive steady-state solutions of a predator-prey system with non-monotonic functional response, also called Holling type-IV interaction terms, and diffusion under the homogeneous Neumann boundary condition. We first establish positive upper and lower bounds for such solutions, and then study their non-existence, global existence and bifurcation.

Keywords

predator-prey modelnon-constant positive steady statesbifurcationglobal existence35J5592D25
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 88 , Issue 1 , January 2004 , pp. 135 - 157
Copyright
2004 London Mathematical Society

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Footnotes

The work of the first author was supported by the NUS ARF Grant R-146-000-034-112.
Part of the paper was prepared during the visit of the second author to the National University of Singapore. He expresses his gratitude for the support of the NUS ARF Grant R-146-000-034-112, and PRC NSF Grant NSFC-19831060 and the ‘333’ Project of JiangSu Provice, China.