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

Abstract

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 stable phase in both microscopic and macroscopic cases. It is shown that the fluctuation effect plays an important rule in the microscopic approach while it is negligible in the macroscopic case.

Keywords

• reaction-diffusion systems
• bistable system
• schlögl model
• pattern formation
• cellular automata