Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion

Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model

and Applied Analysis 3 If b > h, from the second equation of model (6), one has: . v ≤ v (b − h − hmv) . (9) A standard comparison argument shows that lim sup t→∞ v (t) ≤ b − h hm ≜ α. (10) If b ≤ h, we have the following differential inequality: . v ≤ −hmv2 mv + 1 , (11) and the same argument above yields lim sup t→∞ v (t) ≤ 0. (12) In either case, the second inequality of (7) holds. 2.2. Boun...

Spatial patterns of a predator-prey model with cross diffusion

In this paper, spatial patterns of a Holling– Tanner predator-prey model subject to cross diffusion, which means the prey species exercise a self-defense mechanism to protect themselves from the attack of the predator are investigated. By using the bifurcation theory, the conditions of Hopf and Turing bifurcation critical line in a spatial domain are obtained. A series of numerical simulations ...

Instability Induced by Cross-Diffusion in a Predator-Prey Model with Sex Structure

Cross-diffusion induced stationary patterns in a prey-predator system with parental care for predators

A stage structure is incorporated into a prey-predator model in which predators are split into immature predators and mature predators. It is assumed that immature predators are raised by their parents in the sense that they cannot catch the prey and their foods are provided by parents. Further, it is assumed that the maturation rate of immature predators is a function of the food availability ...

Bifurcation analysis of a predator–prey system with self- and cross-diffusion and constant harvesting rate

In this paper, we focus on a ratio dependent predator–prey system with selfand cross-diffusion and constant harvesting rate. By making use of a brief stability and bifurcation analysis, we derive the symbolic conditions for Hopf, Turing and wave bifurcations of the system in a spatial domain. Additionally, we illustrate spatial pattern formations caused by these bifurcations via numerical examp...