in this work the mathematical model of a spatial pattern inchemical and biological systems is investigated numerically. theproposed model considered as a nonlinear reaction-diffusionequation. a computational approach based on finite difference andrbf-collocation methods is conducted to solve the equation withrespect to the appropriate initial and boundary conditions. theability and robustness o...

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 of ...

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

The stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use Markovian jumps to model stochastic reaction diffusion systems‎. ‎In this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps‎. ‎Under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

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 ...

Singular limit problems of reaction-diffusion systems have been studied in cases where the effects reaction terms are very large compared with those other terms. Such appear literature various fields such as chemistry, ecology, biology, geology and approximation theory. In this paper, we deal singular a general system including many literature. We formulate problem,...