Abstract
The main goal of this paper is investigating the existence of nonconstant positive steady states of a linear prey–predator cross-diffusion system with Beddington–DeAngelis and Tanner functional response. An analytical method and fixed point index theory plays a significant role in our main proofs.
Highlights
IntroductionThe smooth functions u0 and v0 on represent the initial population densities of prey and predator
1 Introduction We propose and study a predator–prey cross-diffusion system with the Beddington– DeAngelis and Tanner functional response d1 d3 u – d2 u – d4 v
3 Nonconstant positive steady states we offer a rigorous study of interior solutions of the corresponding strongly coupled elliptic model
Summary
The smooth functions u0 and v0 on represent the initial population densities of prey and predator. With rapid development of biotechnology, we need to accurately illustrate the interaction between prey and predator in a real ecological environment such as hare and lynx, sparrow hawk and sparrow, spider mite and mite, and so on. Such interesting natural phenomena as the existence and global stability of interior periodic solutions and the global stability of reaction–diffusion system have been described by this ODE model [1] or the corresponding PDE system [2].
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