Bicritical scaling behavior in unidirectionally coupled oscillators.
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.
Kim
S Y
SY
Department of Physics, Kangwon National University, Chunchon, Kangwon-Do 200-701, Korea. sykim@cc.kangwon.ac.kr
Lim
W
W