Dynamics of inhomogeneous one--dimensional coupled map lattices (original) (raw)

2004, Arxiv preprint nlin/0409014

Abstract

We study the dynamics of one-dimensional discrete models of one-component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities ("defects") are treated in terms of parameter difference in the corresponding maps. Two types of space defects are considered: periodic and localized. We elaborate analytic approach to obtain the regions with the qualitatively different behaviour in the parametric space. For the model with space-periodic nonhomogeneities we found an exact boundary separating the regions of regular and chaotic dynamics. For the chain with a unique (localized) defect the numerical estimate is given. The effect of the nonhomegeneity on the global dynamics of the system is analyzed.

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