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turing patterns in a Reaction-Diffusion System

Communications in Theoretical Physics 2006年第4期45卷 761-764页

作者： WU Yan-Ning WANG Ping-Jian HOU Chun-Ju LIU Chang-Song ZHU Zhen-Gang Key Laboratory of Material Physics Institute of Solid State Physics the Chinese Academy of Sciences P.O. Box 1129 Hefei 230031 China

We have further investigated turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple turing patterns and complex superlattice structures are observed. We find that the shape and type of turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel Epstein model Our numerical results provide additional insight into understanding the mechanism of development of turing patterns and predicting new pattern formations.

关键词： turing pattern Lengyel-Epstein (LE) model

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CROSS-DIFFUSION INDUCED turing patternS IN A SEX-STRUCTURED PREDATOR-PREY MODEL

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International Journal of Biomathematics 2012年第4期5卷 39-61页

作者： JIA LIU HUA ZHOU LAI ZHANG College of Mathematics and Physics Changzhou University Changzhou 213016 P. R. China Department of Mathematics The Technical University of Denmark DK 2800 Lyngby Denmark

In this paper, we consider a sex-structured predator prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of turing patterns are derived.

关键词： Predator-prey model cross-diffusion turing pattern sex structure.

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Study of turing patterns in a SI reaction-diffusion propagation system based on network and non-network environments

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International Journal of Biomathematics 2024年第1期17卷 199-225页

作者： Yuxuan Tang Shuling Shen Linhe Zhu School of Mathematical Sciences Jiangsu University Zhenjiang212013P.R.China Department of Stomatology Afiliated Hospital of Jiangsu University Zhenjiang 210008P.R.China

The study of rumor propagation dynamics is of great significance to *** news and ensure the authenticity of news *** this paper,a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is ***,through stability analysis,we obtain the conditions for the existence and local stability of the positive equilibrium *** selecting suitable variable as the control parameter,the critical value of turing bifurcation and the existence theorem of turing bifurcation are ***,using the above theorem and multi-scale standard analysis,the expression of amplitude equation around turing bifurcation point is *** analyzing the amplitude equation,different types of turing pattern are divided such as uniform steady-state mode,hexagonal mode,stripe mode and mixed structure ***,in the numerical simulation part,by observing different patterns corresponding to different values of control variable,the correctness of the theory is ***,the effects of different network structures on patterns are *** results show that there are significant differences in the distribution of users on different network structures.

关键词： Reaction-diffusion system rumor propagation amplitude equation turing pattern

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Recovery of the scale-ε2 pattern by lattice BGK model

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Communications in Nonlinear Science and Numerical Simulation 2001年第1期6卷 40-44页

作者： Guangwu YAN and Li YUAN (Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Department of mathematics, Jinn University, Chongchun 130023, China) Inst. of Computational Mathematics Acad. of Math. and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of Mathematics Jilin University Changchun 130023 China

A lattice BGK method for nonlinear chemical reactions is described. Since the equation does not possess the convect terms, we can easily get the equilibrium distribution functions of the lattice BGK models. Using this... 详细信息

关键词： lattice BGK method turing pattern mosaic structure

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The study of pattern dynamics about some model

The study of pattern dynamics about some model

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第十五届全国非线性振动暨第十二届全国非线性动力学和运动稳定性学术会议

作者：郑前前 Shen Jianwei School of Mathematics and Statistics Zhengzhou University School of Mathematics and Statistics Xuchang University

turing bifurcation,amplitude equation and secondary bifurcation play an important role in studying pattern *** some way,the shape of pattern means the distribution of the concentration of some element in *** addition,diffusion and cross-diffusion are all able to destabilize the uniform equilibrium,and have influence on the shape of pattern,which help us how to understand the emergence of *** I will simply show them in some model.

关键词： turing pattern stability bifurcation line

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