某类离散反应扩散系统图灵斑图.docx

The Turing Spot Diagram Of Discrete Reaction Diffusion System
ABSTRACT
The mathematical mechanism description on Turing spot diagram , usually means that the stability constant equilibrium of the system occurs reversely after joining diffusion, generates Turing spot diagram nearby, then use certain model to realize this process, and leads to parameter conditions required of Turing spot diagram .According to the literature, in Turing instability analysis, people often give theoretical analysis to the continuum model , while the Turing spot diagram simulation undoubtedly adopt corresponding discretization model. And there is extremely little discrete model Turing spot diagram analysis. This paper will give the Turing instability circumstance analysis, selecting some discrete reaction diffusion model, through the use of some mathematical method and puter simulation.
In the second chapter, we analyze some typical properties of Lotka - Volterra model and obtain several new discrete model through the approach of mixture discrete.
In the third chapter, we analyze the spot diagram structure of the hybrid discrete model , analyze several unstable conditions of hybrid discrete reaction diffusion system , and obtain the corresponding Turing spot graph parameter space.
In the fourth chapter, we choose appropriate parameters puter simulation of discrete reaction diffusion system Turing spot diagram. Get such Lotka - Volterra discrete reaction diffusion system structure of the spot diagram when diffusion exists, Finally discuss the selection problem of related parameters in the system.
Finally we summarize the work of this paper and put forward the prospects for a follow-up study.
Keywords: Turing spot diagram, Lotka - Volterra model, discrete reaction diffusion system
目 录
第一章 引言
1 . 1 研究意义………………………………………………… 1
1 . 2 国内外研究概况…………………………………………… 2
1 . 3 本文主要的工作……………………………………………… 4
第二章 离散 Lotka-Volterra 模型的获得
2. 1 典型 Lotka-Volterra 模型…………………………………………………6
2. 2 混合 Lotka-