American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 268-279. doi: 10.3934/proc.2005.2005.268

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

Wei Feng 1, and  Jody Hinson 2,

1. 

Department of Mathematics and Statistics, University of North Carolina in Wilmington, Wilmington, NC 28403
2. 

Mathematics and Statistics, University of North Carolina at Wilmington, 601 S. College Rd, Wilmington, NC 28403, United States

Received  September 2004 Revised  May 2005 Published  September 2005

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, Stability and asymptotic behavior., time delays.
Mathematics Subject Classification: Primary: 35K55, 35B40; Secondary: 92B0.
Citation: Wei Feng, Jody Hinson. Stability and pattern in two-patch predator-prey population dynamics. Conference Publications, 2005, 2005 (Special) : 268-279. doi: 10.3934/proc.2005.2005.268
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