Affiliation:
1. Department of Mathematics, Nova Southeastern University, Ft. Lauderdale, FL, USA
2. Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD, USA
Abstract
This paper concerns spatio-temporal pattern formation in a model for two competing prey populations with a common predator population whose movement is biased by direct prey-taxis mechanisms. By pattern formation, we mean the existence of stable, positive non-constant equilibrium states, or nontrivial stable time-periodic states. The taxis can be either repulsive or attractive and the population interaction dynamics is fairly general. Both types of pattern formation arise as one-parameter bifurcating solution branches from an unstable constant stationary state. In the absence of our taxis mechanism, the coexistence positive steady state, under suitable conditions, is locally asymptotically stable. In the presence of a sufficiently strong repulsive prey defense, pattern formation will develop. However, in the attractive taxis case, the attraction needs to be sufficiently weak for pattern formation to develop. Our method is an application of the Crandall–Rabinowitz and the Hopf bifurcation theories. We establish the existence of both types of branches and develop expressions for determining their stability.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology,Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献