Stability of non-monotone waves in a three-species reaction—diffusion model

DOI10.1017/S0308210500027499zbMath0937.35089MaRDI QIDQ4243033

Patrick D. Miller

Publication date: 7 June 2000

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

asymptotic stabilityLotka-Volterra nonlinearitiestravelling wave ansatztwo slow and four fast components

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57)

Related Items (6)

Nonexistence of traveling wave solutions, exact and semi-exact traveling wave solutions for diffusive Lotka-Volterra systems of three competing species ⋮ The stability of traveling waves with non-critical speeds for some competition systems ⋮ Existence of front-back-pulse solutions of a three-species Lotka-Volterra competition-diffusion system ⋮ Traveling waves in a three species competition-cooperation system ⋮ The existence and stability of travelling waves with transition layers for some singular cross-diffusion systems ⋮ The existence and stability of traveling waves with transition layers for the S-K-T competition model with cross-diffusion

Cites Work

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• Existence and stability of travelling wave solutions of competition models. A degree theoretic approach
• Geometric theory of semilinear parabolic equations
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Nonmonotone waves in a three species reaction-diffusion model
• Stability of Travelling Wave Solutions of Diffusive Predator-Prey Systems
• Stability and Hopf Bifurcation of Steady State Solutions of a Singularly Perturbed Reaction-Diffusion System

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