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Bicritical scaling behavior in unidirectionally coupled oscillators.

Abstract

We study the scaling behavior of period doublings in a system of two unidirectionally coupled parametrically forced pendulums near a bicritical point where two critical lines of period-doubling transition to chaos in both subsystems meet. When crossing a bicritical point, a hyperchaotic attractor with two positive Lyapunov exponents appears, i.e., a transition to hyperchaos occurs. Varying the control parameters of the two subsystems, the unidirectionally coupled parametrically forced pendulums exhibit multiple period-doubling transitions to hyperchaos. For each transition to hyperchaos, using both a "residue-matching" renormalization group method and a direct numerical method, we make an analysis of the bicritical scaling behavior. It is thus found that the second response subsystem exhibits a new type of non-Feigenbaum scaling behavior, while the first drive subsystem is in the usual Feigenbaum critical state. The universality of the bicriticality is also examined for several different types of unidirectional couplings.

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BibTeXRIS

S Y Kim, W Lim. 2001-02-27. Bicritical scaling behavior in unidirectionally coupled oscillators.. https://doi.org/10.1103/physreve.63.036223

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