Dynamical Behavior of Coupled Chaotic Oscillators and its Control

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As a model of coupled nonlinear oscillators, a periodic coupled map lattice (CML) composed of J lattice points are numerically examined. In this system, the logistic map is chosen as the local dynamics, and the nonlinearity parameter of this map is reduced to b for every Mth lattice points from 2 for other lattice points. These lattice points are diffusively coupled with the coupling constant epsilon. If J is large enough to satisfy the conditions J <greater than or equal> 5M the phase diagram on the (b, epsilon) plane depends on J only weakly except for a smalIn the phase diagrams, we find a few regions, called Regions A, B and C, in which the pattern selection is observed. Although Region A, found for small epsilon, extends from b = 0 to b = 2 which corresponds to the case of a homogeneous CML, Regions B and C, found for larger epsilon, extend only up to a certain b which is smaller than 2. Outside these regions, we usually observe the spatiotemporal chaos. Therefore, when M is not so large, the introduction of the periodicity can suppress the spatiotemporal chaos to the pattern selection for epsilon within Regions B and C if b is sufficiently small.It is also found that the transient length Nt, the time step at which a solution of the periodic CML reaches the pattern selection from a random initial state, increases with M roughly exponentially in Regions B and C and algebraically in Region A if b is sufficiently smaller than 2. Therefore, although the suppression of the spatiotemporal chaos is realized with smaller modification of the homogeneous CML if we choose larger M, the time step required for the attainment of this suppression from a random initial state becomes much larger.Furthermore, the pattern formation in Faraday waves is examined as a typical example of nonlinear extended system.