Stochastic Resonance-Like Behavior in the Sine-Circle Map

概要

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In the sine-circle map, the phase-locking structure on the parameter plane (Ω, K) is known as Arnold's tongue. The overlapping of two adjacent tongues implies the coexistence of two phase-locked attractors with different rotation numbers. The phase-locked attractors are destroyed by crisis, and the lines of crisis are observed on the parameter plane. At the intersecting point of the two crisis lines associated with two adjacent tongues, the coexisting phase-locked attractors are simultaneously destroyed by crisis. Along a curve passing through this intersecting point, a transition from the two phase-locked attractor into a phase-unlocked attractor is observed. Along such a curve, the response to the external weak periodic forcing is investigated by observing the signal to noise ratio (SNR). The well-known formula SNR ∝ D^<-2> exp(-c/D) for the stochastic resonance is compared with the numerical result, where the noise strength D is introduced through the characteristic time of the switching between the two regions where the two phase-locked attractors lie before the transition to a phaseunlocked attractor.
理論物理学刊行会の論文
1999-12-25