Extremely Weak Feedback Method for Controlling Chaotic Resonance

Chaotic resonance, resembling stochastic resonance, is induced by internal fluctuations (i.e., chaos). This phenomenon has been observed in numerous systems. The most representative form of chaotic resonance is the synchronization with respect to weak applied signals under chaos-chaos intermittency, where a chaotic orbit moves among multiple attractors. Chaotic resonance exhibits higher sensitivity than stochastic resonance, but its engineering applications are limited by concerns such as the requirement to adjust the state of chaos by internal system parameters to induce chaotic resonance rather than the external noise strength. However, achieving this adjustment is challenging, especially in biological systems. Therefore, to handle this limitation, we proposed a novel double-Gaussian-filtered reduced region of orbit (RRO) method (called the DG-RRO method) for obtaining perturbed feedback signals lower than the conventional RRO method. This DG-RRO feedback signal is determined by the inverse sign of the map function and double-Gaussian filters around the local maximum/minimum values of the map. Because of its fine local specification, the DG-RRO feedback signal induces a chaotic resonance by one-third the feedback strength of the conventional signal. This method may pave the way for using chaotic resonance in engineering applications.