Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System

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

Turing instability for a ratio-dependent predator-prey model with diffusion

Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence and stability properties of the equilibrium solutions in a reaction-diffusion model in which predator mortality is neither a constant nor an unbounded functio...

Diffusion-Induced Chaos in a Spatial Predator--Prey System

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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...

Coevolution in a One Predator–Two Prey System

BACKGROUND Our understanding of coevolution in a predator-prey system is based mostly on pair-wise interactions. METHODOLOGY AND PRINCIPAL FINDINGS Here I analyze a one-predator-two-prey system in which the predator's attack ability and the defense abilities of the prey all evolve. The coevolutionary consequences can differ dramatically depending on the initial trait value and the timing of t...