Persistence for a Two-Stage Reaction-Diffusion System

Fast-reaction asymptotics for a two-scale reaction-diffusion system

We investigate a reaction–diffusion process in a two-phase medium with microscopic length scale ε. The diffusion coefficients in the two phases are highly different (d1/D = ε2) and the reaction constant k is large. First, the homogenisation limit ε → 0 is taken, which leads to a two-scale model. Afterwards, we pass to the fast-reaction limit k →∞ and obtain a two-scale reaction-diffusion system...

A stage-structured delayed reaction-diffusion model for competition between two species

A STAGE-STRUCTURED DELAYED REACTION-DIFFUSION MODEL FOR COMPETITION BETWEEN TWO SPECIES

A two-scale reaction-diffusion system with micro-cell reaction concentrated on a free boundary

We discuss the fast-reaction limit of a two-scale reaction-diffusion model. We point out that if the reaction constant a explodes to infinity, then a two-scale PDEs system with free boundary at the micro cell is obtained. The aim of this note is to answer the question: Can the same two-scale free-boundary problem be obtained if we first pass to the fast-reaction limit a → ∞ and then take the ho...

Chapter 7 Two-Dimensional Reaction-Diffusion Brusselator System

Cellular Automata Simulation of a Bistable Reaction-Diffusion System: Microscopic and Macroscopic Approaches

The Cellular Automata method has been used to simulate the pattern formation of the Schlögl model as a bistable Reaction-Diffusion System. Both microscopic and macroscopic Cellular Automata approaches have been considered and two different methods for obtaining the probabilities in the microscopic approach have been mentioned. The results show the tendency of the system towards the more sta...