Selection of windows, attractors and self-similar patterns in a coupled map lattice |
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Authors: | Frederick H Willeboordse |
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Institution: | Institute of Physics, University of Tsukuba, Ibaraki 305., Japan |
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Abstract: | It is shown that a lattice of diffusively coupled logistic maps displays self-similar period-doubling cascades to chaos with all the known stages of pattern formation. The location of the self-similar patterns is determined. The basins of attraction yielding window structures, so far believed to be negligibly small, are shown to cover virtually all initial conditions given a certain maximum amplitude to the random initial conditions. As a consequence a means for selecting attractors in a CML is obtained. A new pattern selection regime at high nonlinearity is reported and the basins of attraction of some attractors of small lattices are investigated. |
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