Pattern Formation in Reaction-Diffusion Systems

Pattern Formation of the FitzHugh-Nagumo Model: Cellular Automata Approach

FitzHugh-Nagumo (FHN) model is a famous Reaction-Diffusion System which first introduced for the conduction of electrical impulses along a nerve fiber. This model is also considered as an abstract model for pattern formation. Here, we have used the Cellular Automata method to simulate the pattern formation of the FHN model. It is shown that the pattern of this model is very similar to those...

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...

A numerical treatment of a reaction-diffusion model of spatial pattern in the embryo

In this work the mathematical model of a spatial pattern in chemical and biological systems is investigated numerically. The proposed model considered as a nonlinear reaction-diffusion equation. A computational approach based on finite difference and RBF-collocation methods is conducted to solve the equation with respect to the appropriate initial and boundary conditions. The ability and robust...

Reaction-Diffusion Systems in Pattern Formation and Pattern Recognition Processes

This paper presents a quick review of reaction-diffusion systems that self-organize spatio-temporal patterns in chemical and biological systems. A pair of reaction-diffusion equations having activator and inhibitor variables is a typical model of equations describing their pattern formation processes. Some of the reaction-diffusion systems can realize several functions of image processing such ...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Spatio-temporal Pattern Formation in Reaction-diffusion Systems Coupled with Convection and Geometrical Effect

To understand how living organisms maintain their lives, it is important to regard the living organisms as nonequilibrium open systems, since organisms live through the dissipation of the chemical energy of the nutrition. So far, a number of studies on physics under nonequilibrium open conditions have been performed both experimentally and theoretically. Among these studies, spatiotemporal self...