Journal
PRAMANA-JOURNAL OF PHYSICS
Volume 82, Issue 6, Pages 995-1009Publisher
INDIAN ACAD SCIENCES
DOI: 10.1007/s12043-014-0753-2
Keywords
Chaos; coupled map lattice; partial differential equation; higher dimension
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Funding
- Foundation for the National Natural Science Foundation of China [61273088]
- Shandong University of Political Science and Law [2013Q07B]
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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.
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