Coherence resonance in chaotic systems

– We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose regularity is optimal for some intermediate value of the noise intensity. We find that the power spectrum of the signal develops a peak at finite frequency at intermediate values of the noise. These are all signatures of coherence resonance. We also experimentally study a Chua circuit and corroborate the above simulation results. Finally, we analyze a simple model composed of two separate limit cycles which still exhibits coherence resonance, and show that its behavior is qualitatively similar to that of the chaotic Chua system. When a dynamical system is subjected to an external periodic forcing, it is a standard result that synchronization between the system and the forcing can occur under a large variety of conditions. A resonance is defined as the presence of a maximum in the response of the system as a function of some control parameter (for instance, the frequency of the external signal). Although one might naively believe that fluctuations, either in the forcing or in the intrinsic dynamics, will worsen the quality of the synchronization, it is nowadays well established that, in some cases, the response of a nonlinear dynamical system to an external forcing can be enhanced by the presence of noise (fluctuations). The prototypical and pioneering example is that of stochastic resonance [1,2] by which a bistable system under the influence of a periodic forcing, and in the presence of fluctuations, shows an optimum response, a resonance, for a given value of the noise intensity. The relevance of this phenomenon has been shown for some physical and biological systems described by a nonlinear dynamics [3–5]. (∗) Permanent address: Department of Physics, Lehigh University Bethlehem, PA 18015, USA.