Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space

Pramana

Li Zhang1¹  Shutang Liu³  Chenglong Yu² 

[1] Business School, Shandong University of Political Science and Law, Jinan 250014, China$$;Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, IL 60607-7045, USA$$;College of Control Science and Engineering, Shandong University, Jinan 250061, China$$

关键词: Chaos;    coupled map lattice;    partial differential equation;    higher dimension.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In recent years, nonlinear coupled reaction–diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two- and three-dimensional spaces.

【 授权许可】

Unknown