斑图动力学

第一章，介绍了反应扩散系统及其斑图动力学研究背景和现状，并简单综述了Gray-Scott模型和捕食系统斑图动力学的研究成果。

The first chapter , we introduce the background and current situation of reaction-diffusion systems and pattern formation . And we briefly analyze the research of the Gray-Scott model and biological prey-predator system dynamics .

图灵斑图动力学的数学机制

Mathematical Mechanism of Turning Pattern Dynamics

这些是斑图动力学（非线性科学邻域内的一个重要分支）研究的主要内容。

These are principal content of pattern formation which is an important branch of nonlinear science .

斑图动力学作为一门横向学科的出现，是随着非线性科学的发展而逐渐形成的。

Pattern dynamics appeared as a transverse science form gradually along with the development of nonlinear science .

光学斑图动力学主要包括激光器斑图动力学和含有非线性介质的光学谐振腔系统的斑图动力学。

Optical pattern dynamics is mainly divided into two parts : laser pattern dynamics and pattern dynamics in optical resonator with nonlinear material .

时变扩散系数是影响反应扩散系统动力学性质的重要因素，也是斑图动力学研究的热点和难点之一。

Time-varying diffusivity is a major factor for the reaction-diffusion system dynamics . And also it is the hot and difficult research point of pattern dynamics .

非线性扩散方程的求解是流体力学、传热学、生物学、化学和斑图动力学等领域的一个热门研究课题。

It has become a hot problem to obtain solutions of nonlinear diffusion equations involving the fluid dynamics , heat transfer , biology , chemistry and pattern dynamics .

本论文章节和结构安排如下：第一章是绪论，简单介绍了斑图动力学理论、反应扩散系统以及螺旋波的形成过程，并说明了计算机数值模拟中常用的几个偏微分方程模型。

This thesis chapters and structure are arranged as follows : The pattern dynamics theory , reaction-diffusion system and the formation of spiral wave are introduced briefly in Chapter 1 .

近几十年来，时空斑图动力学一直是非线性科学研究的热点，通过对他们的研究，有助于了解发生在自然界和人类社会中的现象。

In recent decades , the investigation of spatiotemporal pattern dynamics has become a hot topic of nonlinear science . The investigation can help us to understand the phenomena that occur in nature and human society .

给出图灵斑图动力学数学机制的描述，即常微系统的稳定常数平衡态在加入扩散后发生稳定性反转，在其附近会产生图灵斑图。

In this paper we give the mathematical mechanism of Turning pattern dynamics , that is when a constant equilibrium point of ODE changes its stability property after diffusion introduced , Turning pattern would appear around it .

本文主要通过数值模拟和理论分析的方法，研究了振荡与可激发反应扩散系统中耦合螺旋波斑图的动力学行为。

In this thesis , we numerically and theoretically study the dynamic behaviors of coupled spiral wave patterns in both oscillatory and excitable reaction-diffusion systems .

因此，对螺旋波和时空混沌的控制研究具有很大应用价值，但要彻底解决抑制心脏中螺旋波和时空混沌问题，依赖我们对时空斑图的动力学的彻底了解。

Therefore , study on the control of spiral wave and spatiotemporal chaos is of great value of application . However , it relies on our thorough understanding of the dynamics of the spatiotemporal pattern to solve completely the suppression of spiral wave and spatiotemporal in cardiac tissues .

（1+2）维斑图方程的动力学性态

Dynamical behavior of the ( 1 + 2 ) D pattern formation

采用光学方法，着重对斑图放电的时空动力学进行了系统的实验研究。

The spatiotemporal dynamics of patterned discharges is studied experimentally by an optical method .

该工作对控制斑图的形成和研究斑图动力学具有重要参考价值。电化学斑图中空间耦合的时空动力学

This work gives useful reference for studying pattern formation dynamics . The Spatiotemporal Dynamics in Electrochemical Pattern with Spatial Coupling