Chaotic Resonance in Forced Chua^|^apos;s Oscillators

Abstract

Stochastic resonance (SR) is a phenomenon in which dynamic noise is effectively used to induce state transitions in a double-well potential system driven by subthreshold input signals. The noises are supplied to the system as an additional force. Recently, a phenomenon called "chaotic resonance" (CR) has been spotlighted in the literature. CR can be observed in chaotic systems that have multiple strange attractors and the ability to accept subthreshold input signals; i.e., such CR systems do not require any external noise source, unlike traditional SR systems. In this study, we employed Chua's oscillator as a candidate CR system. The oscillator was driven by a sinusoidal voltage source providing subthreshold input signals. In a certain range of input signal frequencies, we observed chaotic state transitions between the two attractors, whereas no state transition between the attractors was observed in the remaining frequency range. These findings indicated that chaotic fluctuations assisted the state transition. Furthermore, we observed nonmonotonic CR characteristics (correlation value and signal-to-noise ratio between the input signal and the output signal) that corresponded to typical nonmonotonic SR curves.

Controlling Chaotic Resonance using External Feedback Signals in Neural Systems

“…In these systems, the timing of chaos–chaos intermittency is synchronised with weak external input signals by adjusting internal system parameters. At first, this phenomenon was evaluated in simple models and electrical circuits, such as one-dimensional cubic maps, Lorenz models, and Chua’s circuit 2 , 26 – 28 , 30 . Since these studies, the exploration of chaotic resonance in neural system has progressed 31 – 34 .…”

Chaotic resonance in Izhikevich neural network motifs under electromagnetic induction

“…Chew et al [29] considered the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation. Kazuyoshi et al [34] studied CR in forced Chua's oscillators. A large number of studies further show the universality and importance of CR [7].…”