Stochastic resonance (SR) is a phenomenon in which signal response in a nonlinear system is enhanced by noise. Fluctuating activities in deterministic chaos are known to cause a phenomenon called chaotic resonance (CR), which is similar to SR. Most previous studies on CR showed that these signal responses were controlled by internal parameters. However, in several applications of CR, it is difficult to control these parameters externally, particularly in biological systems. In this study, to overcome this difficulty, we propose a method for controlling the signal response of CR by adjusting the strength of external feedback control. By using this method, we demonstrate the control of CR in a one-dimensional cubic map, where CR arises from chaos-chaos switching to a weak input signal.

It is well-known that chaos synchronization in coupled chaotic systems arises from conditions with specific coupling, such as complete, phase, and generalized synchronization. Recently, several methods for controlling this chaos synchronization using a nonlinear feedback controller have been proposed. In this study, we applied a proposed reducing range of orbit feedback method to coupled cubic maps in order to control synchronization of chaos-chaos intermittency. By evaluating the system's behavior and its dependence on the feedback and coupling strength, we confirmed that synchronization of chaos-chaos intermittency could be induced using this nonlinear feedback controller, despite the fact that the asynchronous state within a unilateral attractor is maintained. In particular, the degree of synchronization is high at the edge between the chaos-chaos intermittency parameter region for feedback strength and the non-chaos-chaos intermittency region. These characteristics are largely maintained on large-scale coupled cubic maps.

Various types of synchronization phenomena have been reported in coupled chaotic systems. In recent years, the applications of these phenomena have been advancing for utilization in sensor network systems, secure communication systems, and biomedical systems. Specifically, chaos-chaos intermittency (CCI) synchronization is a characterized synchronization phenomenon. Previously, we proposed a new chaos control method, termed as the “reduced region of orbit (RRO) method,” to achieve CCI synchronization using external feedback signals. This method has been gathering research attention because of its ability to induce CCI synchronization; this can be achieved even if internal system parameters cannot be adjusted by external factors. Further, additive stochastic noise is known to have a similar effect. The objective of this study was to compare the performance of the RRO method and the method that applies stochastic noise, both of which are capable of inducing CCI synchronization. The results showed that even though CCI synchronization can be realized using both control methods under the induced attractor merging condition, the RRO method possesses higher adoptability and accomplishes a higher degree of CCI synchronization compared to additive stochastic noise. This advantage might facilitate the application of synchronization in coupled chaotic systems.

Fluctuations in nonlinear systems can enhance the synchronization with weak input signals. These nonlinear synchronization phenomena are classified as stochastic resonance and chaotic resonance. Many applications of stochastic resonance have been realized, utilizing its enhancing effect for the signal sensitivity. However, although some studies showed that the sensitivity of chaotic resonance is higher than that of stochastic resonance, only few studies have investigated the engineering application of chaotic resonance. A possible reason is that, in chaotic resonance, the chaotic state must be adjusted through internal parameters to reach the state that allows resonance. In many cases and especially in biological systems, such adjustments are difficult to perform externally. To overcome this difficulty, we developed a method to control the chaotic state for an appropriate state of chaotic resonance by using an external feedback signal. The method is called reducing the range of orbit (RRO) feedback method. Previously, we have developed the RRO feedback method for discrete chaotic systems. However, for applying the RRO feedback method to actual chaotic systems including biological systems, development of the RRO feedback signals in continuous chaotic systems must be considered. Therefore, in this study, we extended the RRO feedback method to continuous chaotic systems by focusing on the map function on the Poincaré section. We applied the extended RRO feedback method to Chua's circuit as a continuous chaotic system. The results confirmed that the RRO feedback signal can induce chaotic resonance. This study is the first to report the application of RRO feedback to a continuous chaotic system. The results of this study will facilitate further device development based on chaotic resonance.

Recent developments in engineering applications of stochastic resonance have expanded to various fields, especially biomedicine. Deterministic chaos generates a phenomenon known as chaotic resonance, which is similar to stochastic resonance. However, engineering applications of chaotic resonance are limited owing to the problems in controlling chaos, despite its uniquely high sensitivity to weak signal responses. To tackle these problems, a previous study proposed “reduced region of orbit” (RRO) feedback methods, which cause chaotic resonance using external feedback signals. However, this evaluation was conducted under noise-free conditions. In actual environments, background noise and measurement errors are inevitable in the estimation of RRO feedback strength; therefore, their impact must be elucidated for the application of RRO feedback methods. In this study, we evaluated the chaotic resonance induced by the RRO feedback method in chaotic neural systems in the presence of stochastic noise. Specifically, we focused on the chaotic resonance induced by RRO feedback signals in a neural system composed of excitatory and inhibitory neurons, a typical neural system wherein chaotic resonance is observed in the presence of additive noise and feedback signals including the measurement error (called contaminant noise). It was found that for a relatively small noise strength, both types of noise commonly degenerated the degree of synchronization in chaotic resonance induced by RRO feedback signals, although these characteristics were significantly different. In contrast, chaos-chaos intermittency synchronization was observed for a relatively high noise strength owing to the noise-induced attractor merging bifurcation for both types of noise. In practical neural systems, the influence of noise is unavoidable; therefore, this study highlighted the importance of the countermeasures for noise in the application of chaotic resonance and utilization of noise-induced attractor merging bifurcation.