Chaos-Chaos Intermittency Synchronization Controlled by External Feedback Signals in Chua's Circuits

Sou NOBUKAWA  Hirotaka DOHO  Natsusaku SHIBATA  Haruhiko NISHIMURA  Teruya YAMANISHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.1   pp.303-312
Publication Date: 2020/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1081
Type of Manuscript: PAPER
Category: Nonlinear Problems
Keyword: 
synchronization,  chaotic resonance,  chaos-chaos intermittency,  control,  

Full Text: FreePDF(5.1MB)


Summary: 
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.