Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis

doi:10.1088/1674-1056/19/10/100509

中国物理B ›› 2010, Vol. 19 ›› Issue (10): 100509-100509.doi: 10.1088/1674-1056/19/10/100509

Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis

占萌¹, 邹为²

(1)Wuhan Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan 430071, China; (2)Wuhan Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan 430071, China; Graduate School of the Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2010-01-18 修回日期:2010-04-09 出版日期:2010-10-15 发布日期:2010-10-15
基金资助:
Project partially supported by the Outstanding Oversea Scholar Foundation of the Chinese Academy of Sciences (Bairenjihua) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis

Zou Wei(邹为)^a)b) and Zhan Meng(占萌)^a)†ger

^a Wuhan Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan 430071, China; ^b Graduate School of the Chinese Academy of Sciences, Beijing 100049, China

Received:2010-01-18 Revised:2010-04-09 Online:2010-10-15 Published:2010-10-15
Supported by:
Project partially supported by the Outstanding Oversea Scholar Foundation of the Chinese Academy of Sciences (Bairenjihua) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

摘要/Abstract

摘要： This paper theoretically analyses and studies stationary patterns in diffusively coupled bistable elements. Since these stationary patterns consist of two types of stationary mode structure: kink and pulse, a mode analysis method is proposed to approximate the solutions of these localized basic modes and to analyse their stabilities. Using this method, it reconstructs the whole stationary patterns. The cellular mode structures (kink and pulse) in bistable media fundamentally differ from stationary patterns in monostable media showing spatial periodicity induced by a diffusive Turing bifurcation.

Abstract: This paper theoretically analyses and studies stationary patterns in diffusively coupled bistable elements. Since these stationary patterns consist of two types of stationary mode structure: kink and pulse, a mode analysis method is proposed to approximate the solutions of these localized basic modes and to analyse their stabilities. Using this method, it reconstructs the whole stationary patterns. The cellular mode structures (kink and pulse) in bistable media fundamentally differ from stationary patterns in monostable media showing spatial periodicity induced by a diffusive Turing bifurcation.

Key words: discrete reaction–diffusion system, stationary patterns, bistable, mode analysis

中图分类号: (Bifurcation theory)

02.30.Oz

05.45.-a (Nonlinear dynamics and chaos)

邹为, 占萌. Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis[J]. 中国物理B, 2010, 19(10): 100509-100509.

Zou Wei(邹为) and Zhan Meng(占萌). Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis[J]. Chin. Phys. B, 2010, 19(10): 100509-100509.

参考文献 31

[1]	Cross M C and Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2]	Kapral R and Showalter K 1995 Chemical Waves and Patterns (Dordrecht: Kluver Academic Publishers)
[3]	Epstein I R and Pojman J A 1998 An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos (New York: Oxford University Press)
[4]	Kuramoto Y 1984 Chemical Oscillations, Waves, and Turbulence (Berlin: Springer)
[5]	Field R J and Burger M 1985 Oscillations and Travelling Waves in Chemical Systems (New York: Wiley-Interscience)
[6]	Keener J and Sneyd J 1998 Mathematical Physiology (New York: Springer-Verlag) Chapter 9
[7]	Murray J D 2003 Mathematical Biology 3rd edn. (Berlin: Springer)
[8]	Gao Z Y and Lu Q S 2007 Chin. Phys. 16 2479
[9]	Wang B Y, Xing Z C and Xu W 2009 Acta Phys. Sin. 58 6590 (in Chinese)
[10]	Turing A M 1952 Philos. Trans. Roy. Soc. London Ser. B bf 237 37
[11]	Castets V, Dulos E, Boissonade J and De Kepper P 1990 Phys. Rev. Lett. 64 2953
[12]	De Kepper P, Castets V, Dulos E and Boissonade J 1991 Physica D 49 161
[13]	Langyel I and Epstein I R 1990 Science bf 251 650
[14]	Ouyang Q and Swinney H L 1991 Nature 352 610
[15]	Kladko K, Mitkov I and Bishop A R 2000 Phys. Rev. Lett. bf 84 4505
[16]	Laplante J P and Erneux T 1992 J. Phys. Chem. 96 4931
[17]	Erneux T and Nicolis G 1993 Physica D 67 237
[18]	F'ath G 1998 Physica D 116 176
[19]	Keener J P 1987 SIAM J. Appl. Math. 47 556
[20]	Comte J C, Morfu S and Marqui'e P 2000 Phys. Rev. E bf 64 027102
[21]	Mitkov I, Kladko K and Pearson J E 1998 Phys. Rev. Lett. bf 81 5453
[22]	Preez-Munuzuri V, Perez-Villar V and Chua L O 1992 Int. J. Bifur. Chaos 2 403
[23]	MacKay R S and Sepulchre J A 1995 Physica D bf 82 243
[24]	Nekorkin V I and Makarov V A 1995 Phys. Rev. Lett. 74 4819
[25]	Mu nuzhi A P and Chua L O 1997 Int. J. Bifur. Chaos bf 7 2807 % locally linearly coupled
[26]	Nizhnik L P, Nizhnik I L and Hasler M 2002 Int. J. Bifur. Chaos 12 261
[27]	Nagumo J, Arimoto S and Yoshisawa S 1962 Proc. IRE 50 2061
[28]	Paz'o D and P'erez-Mu nuzuri V 2001 Phys. Rev. E bf 64 065203(R)
[29]	Paz'o D and P'erez-Mu nuzuri V 2003 Chaos 13 812
[30]	Parker T S and Chua L O 1989 Practical Numerical Algorithms for Chaotic Systems (New York: Springer-Verlag)
[31]	Liu W Q, Wu Y, Zou W, Xiao J H and Zhan M 2007 Phys. Rev. E 76 036215 endfootnotesize

Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis

Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis

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