Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps |
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Authors: | Hiroyasu Ando Sudeshna Sinha Kazuyuki Aihara |
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Institution: | (1) Aihara Complexity Modelling Project, ERATO, JST, 4-1-8, Honcho, Kawaguchi, Saitama, Japan;(2) The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600 113, India;(3) Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan |
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Abstract: | Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element
has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted
by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest
neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields
clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a
power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/f power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also
interpret the power-law characteristics of the proposed system from an ecological point of view.
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Keywords: | Self-organization power-law scaling chaos control 1/f noise coupled map lattices |
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