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Stability and pattern in two-patch predator-prey population dynamics

Pages: 268 - 279, Issue Special, August 2005

 Abstract        Full Text (235.7K)              

Wei Feng - Department of Mathematics and Statistics, University of North Carolina in Wilmington, Wilmington, NC 28403, United States (email)
Jody Hinson - Mathematics and Statistics, University of North Carolina at Wilmington, 601 S. College Rd, Wilmington, NC 28403, United States (email)

Abstract: In this paper we explore the dynamics of predator-prey interactions in two patches which are coupled by the diffusion of the predator. The purpose of this exploration to find upper and lower bounds for the populations, and to discuss the complexity and stability of the equilibriums. Some of our results relax the conditions, which are given in earlier papers, necessary for stability of the equilibrium solutions associated with this model. Numerical simulations are also provided to graphically demonstrate the population dynamics of this model utilizing some of the relaxed conditions for stability and new conditions for instability.

Keywords:  Reaction-diffusion systems, Food chain models, time delays, Stability and asymptotic behavior.
Mathematics Subject Classification:  Primary: 35K55, 35B40; Secondary: 92B05.

Received: September 2004;      Revised: May 2005;      Published: September 2005.