強制Chua発振器の集団におけるArray-Enhancedカオス共鳴

摘要

Stochastic resonance (SR) is a phenomenon where dynamic noise is effectively used to induce state transitions in a double-well potential system driven by subthreshold external forces. The noises are given 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 which have multiple strange attractors, and have ability to accept external forces to cause transitions between the attractors. In such chaotic systems, chaotic fluctuations, instead of additional noises in SR systems, could effectively be used to cause the at tractor transition, which may result in CR under certain parameter conditions; i.e., such CR systems do not require any external noise source, unlike traditional SR systems. In this research, we employed Chua's oscillator as a possible candidate of CR systems. The oscillator was driven by a sinusoidal voltage source as a subthreshold driving force. In a certain range of the driving force frequencies, we observed chaotic transitions between two operational regions, whereas no transition between the operational regions was observed in the other frequency range, which indicated that chaotic fluctuation certainly assisted the state transition. Furthermore, we observed nonmonotonic CR characteristics (correlation value and signal-to-noise ratio between the driving force and the output signal) that correspond to typical nonmonotonic SR curves. And then, we evaluated an array of forced Chua's oscillators, just like in the single Chua's oscillator and observed the network will enhance correlation value and SNR in CR.%確率共鳴は雑音を有効に利用した現象のひとつとして挙げられる.これは，二重井戸型ポテンシャル等の系に閾値下の微弱な信号が入力されている時に，外部の雑音を効果的に取り込むことによって信号の値が閾値を超え,状態遷移を可能にする現象である.一方で，カオス共鳴が近年注目されている.この現象は，複数のストレンジアトラクターを持ち，閾値下の信号が入力され得るカオス系において観測される.このようなカオス系では，系内部で生成されるカオスのゆらぎを利用する事で状態遷移を起こす為，従来の確率共鳴と異なり，外部雑音が不要である.本研究では，カオス共鳴を起こす条件を満たす系としてChua発振器を用い，閾値下の信号として正弦波電圧を加えてカオス共鳴の観測を行った.ある入力周波数範囲では二つのアトラクター間でカオス的な遷移が起こり，他の範囲では状態が，一方のアトラクターにトラップされることを確認した.これらの動作が，カオス的なゆらぎが状態遷移に寄与していることを示している.さらに，カオス共鳴の度合いと系内部に発生するゆらぎの強さの関係を調べる為に入出力相関値やSNRを算出し，確率共鳴曲線に類似したカオス共鳴の特性が得られた.また，このChua発振器を並列化して共通の閾値下の入力を加えて同様の実験を行い，カオス共鳴下では相関値やSNRが向上する事を確認した.