General conditions for the existence of a “critical point-periodic wave front” connection for reaction-diffusion systems

DOI10.1016/0362-546X(89)90071-0zbMath0684.34052OpenAlexW2027745935MaRDI QIDQ4734152

J. Sabina, J. M. Fraile

Publication date: 1989

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(89)90071-0

zbMATH Keywords

reaction-diffusion systemsLaplace's operatorhyperbolic limit cycleheteroclinic plane wave fronts

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items

A mathematical biologist's guide to absolute and convective instability, Absolute stability and dynamical stabilisation in predator-prey systems, Invasion Generates Periodic Traveling Waves (Wavetrains) in Predator-Prey Models with Nonlocal Dispersal, Two components is too simple: an example of oscillatory Fisher–KPP system with three components

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the existence of periodic travelling wave solutions with large periods in generalized reaction-diffusion systems
• Geometric singular perturbation theory for ordinary differential equations
• Critical manifolds, travelling waves, and an example from population genetics
• Existence of Travelling Wave Solutions of Predator–Prey Systems via the Connection Index
• Traveling Waves in Diffusive Predator–Prey Equations: Periodic Orbits and Point-to-Periodic Heteroclinic Orbits
• Reaction-Diffusion Systems with Explicit Traveling Wave and Transient Solutions
• Plane Wave Solutions to Reaction-Diffusion Equations
• Slowly Modulated Oscillations in Nonlinear Diffusion Processes
• Kinetic conditions for the existence of wave fronts in reaction-diffusion systems