PMID: 11308757Apr 20, 2001Paper

Bicritical scaling behavior in unidirectionally coupled oscillators

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
S Y Kim, Woochang Lim

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.

References

Mar 15, 1991·Physical Review. a·H KookG Schmidt
Jul 15, 1991·Physical Review. a·S Y Kim, B Hu
Apr 15, 1992·Physical Review. a·S Y Kim, D S Lee
Dec 15, 1992·Physical Review. a· de Sousa Vieira MM A Lieberman
Oct 15, 1992·Physical Review. a·S Y Kim, H Kook
Aug 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Y Kim, H Kook
Feb 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Y Kim, K Lee
Aug 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Y Kim, K Lee
Oct 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Y Kim
Nov 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·O Rudzick, A Pikovsky
Jul 25, 1994·Physical Review Letters·F H Willeboordse, K Kaneko
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Y Kim

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Citations

Nov 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S P Kuznetsov, I R Sataev
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sang-Yoon KimBrian Hunt
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J V KapustinaE Mosekilde

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