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

Sou NOBUKAWA; Hirotaka DOHO; Natsusaku SHIBATA; Haruhiko NISHIMURA; Teruya YAMANISHI

doi:10.1587/transfun.2019EAP1081

IEICE TRANSACTIONS on Fundamentals

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

Sou NOBUKAWA, Hirotaka DOHO, Natsusaku SHIBATA, Haruhiko NISHIMURA, Teruya YAMANISHI

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.1 pp.303-312

Publication Date: 2020/01/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2019EAP1081

Type of Manuscript: PAPER

Category: Nonlinear Problems

Authors

Sou NOBUKAWA
  Chiba Institute of Technology
Hirotaka DOHO
  Kochi University,University of Hyogo
Natsusaku SHIBATA
  Chiba Institute of Technology
Haruhiko NISHIMURA
  University of Hyogo
Teruya YAMANISHI
  Fukui University of Technology

Keyword

synchronization, chaotic resonance, chaos-chaos intermittency, control

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Sou NOBUKAWA, Hirotaka DOHO, Natsusaku SHIBATA, Haruhiko NISHIMURA, Teruya YAMANISHI, "Chaos-Chaos Intermittency Synchronization Controlled by External Feedback Signals in Chua's Circuits" in IEICE TRANSACTIONS on Fundamentals, vol. E103-A, no. 1, pp. 303-312, January 2020, doi: 10.1587/transfun.2019EAP1081.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAP1081/_p

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@ARTICLE{e103-a_1_303,
author={Sou NOBUKAWA, Hirotaka DOHO, Natsusaku SHIBATA, Haruhiko NISHIMURA, Teruya YAMANISHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Chaos-Chaos Intermittency Synchronization Controlled by External Feedback Signals in Chua's Circuits},
year={2020},
volume={E103-A},
number={1},
pages={303-312},
abstract={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.},
keywords={},
doi={10.1587/transfun.2019EAP1081},
ISSN={1745-1337},
month={January},}

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TY - JOUR
TI - Chaos-Chaos Intermittency Synchronization Controlled by External Feedback Signals in Chua's Circuits
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 303
EP - 312
AU - Sou NOBUKAWA
AU - Hirotaka DOHO
AU - Natsusaku SHIBATA
AU - Haruhiko NISHIMURA
AU - Teruya YAMANISHI
PY - 2020
DO - 10.1587/transfun.2019EAP1081
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2020
AB - 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.
ER -

IEICE TRANSACTIONS on Fundamentals