Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...

2023年2月13日 · 反应扩散系统（Reaction–diffusion system）是对应于多种物理现象的数学模型。 最常见的是一种或多种化学物质浓度在空间和时间上的变化：物质相互转化的局部化学反应，以及导致物质在空间表面扩散的扩散。

2010年9月24日 · The reaction-diffusion (Turing) model is a theoretical model used to explain self-regulated pattern formation in biology. Although many biologists have heard of this model, a better understanding of the concept would aid its application to many research projects and developmental principles.

A reaction-diffusion system with appropriate nonlinear kinetics can cause instability in a homogeneous, steady-state system and generate stable concentration patterns. This chapter discusses mathematically and thermodynamically …

2024年4月30日 · And finally, despite the simplicity of their mathematical form, reaction-diffusion systems can show strikingly rich, complex spatio-temporal dynamics. Because of these properties, reaction diffusion systems have been used extensively for modeling self-organization of spatial patterns.

Reaction-diffusion (RD) equations arise naturally in systems consisting of many interacting components, (e.g., chemical reactions) and are widely used to describe pattern-formation phenomena in variety of biological, chemical and physical sys-

The simplest way to integrate reaction-diffusion equations is to use the finite-difference method. In this method, we store concentrations at (say) N +1 mesh points spaced by ∆x and numbered 0 to N, and estimate the second derivative of the concentration at every point using these values.

2025年1月17日 · The reaction-diffusion equation is a partial differential equation that describes the change in the concentration of a chemical system in space with respect to time when both diffusion and chemical reactions are occurring.

2023年7月17日 · We show with extensive numerical experiments how the proposed approach can be applied to a variety of problems regarding reaction–diffusion processes and other PDE systems, including forward...

2020年3月3日 · The reaction-diffusion system is naturally used in chemistry to represent substances reacting and diffusing over the spatial domain.