Asymptotic methods for reaction-diffusion systems: past and present.
نویسنده
چکیده
A brief historical survey of the development of asymptotic and analytical methodologies for the analysis of spatio-temporal patterns in reaction-diffusion (RD) and related systems is given. Although far from complete, the bibliography is hopefully representative of some of the advances in this area over the past 40 years. Within the scope of this survey, some of the key research contributions of Lee Segel are highlighted.
منابع مشابه
Combined effect of hall current and chemical reaction on MHD flow through porous medium with heat generation past an impulsively started vertical plate with constant wall temperature and mass diffusion
Unsteady flow with magneto-hydrodynamics and heat generation through porous medium past an impulsively started vertical plate with constant wall temperature and mass diffusion is considered here. The effect studied is a combination of Hall current and chemical reaction. The motivation behind this study is the applications of such kind of problems in industry. In many industrial applications ele...
متن کاملA 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...
متن کاملPositivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations
Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...
متن کاملCellular 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...
متن کاملOn asymptotic stability of Weber fractional differential systems
In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Bulletin of mathematical biology
دوره 68 5 شماره
صفحات -
تاریخ انتشار 2006