Controlling Chaotic Resonance in Systems with Chaos-Chaos Intermittency Using External Feedback

Nobukawa, Sou; Nishimura, Haruhiko; Yamanishi, Tomonori; Doho, Hirotaka

doi:10.1587/transfun.e101.a.1900

Cited by 22 publications

(79 citation statements)

References 39 publications

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“…In our previous studies, we proposed the RRO feedback control for separating the merged attractor in discrete chaotic systems with CCI [38], [43]- [45]. Here, we briefly explain the control method based on the example of cubic map as follows:…”

Section: Fundamental Description Of Rro Feedback Methods In Discrete Mapmentioning

confidence: 99%

“…Here, K and x d indicate the amplitude of RRO feedback control and the point dividing each attractor, respectively. In our previous study [38], [43], we set x d = 0 because the cubic map of Eq. (2) has two symmetric attractor regions, i.e., positive and negative x(t) regions.…”

Section: Fundamental Description Of Rro Feedback Methods In Discrete Mapmentioning

confidence: 99%

“…In contrast, in stochastic resonance cases, the strength of additive noise can be easily controlled. To address 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 technique is called reducing the range of orbit (RRO) feedback method [38]. In the conventional chaos control method, the chaotic states are transferred to stable periodic states and a fixed point by applying external perturbation, such as in the Ott-Grebogi-Yorke method [39], delayed feedback [40], [41], and H ∞ Copyright © 2020 The Institute of Electronics, Information and Communication Engineers control [42].…”

Section: Introductionmentioning

confidence: 99%

“…In the conventional chaos control method, the chaotic states are transferred to stable periodic states and a fixed point by applying external perturbation, such as in the Ott-Grebogi-Yorke method [39], delayed feedback [40], [41], and H ∞ Copyright © 2020 The Institute of Electronics, Information and Communication Engineers control [42]. On the other hand, the RRO feedback method does not eliminate the chaotic behavior and controls the frequency of CCI and attractor-merging bifurcation [38]. In particular, the RRO feedback signal reduces the local maximum and minimum of the map function, which induce CCI, and controls the attractor merging bifurcation.…”

Section: Introductionmentioning

confidence: 99%

“…The RRO feedback method has been adopted to only discrete chaotic systems typified as the discrete cubic map and its assembly [38], [43] and discrete neural systems [44], [45]. However, in the process of applying the RRO feedback method to actual chaotic systems, development of the RRO feedback signals in continuous chaotic systems must be considered.…”

Section: Introductionmentioning

confidence: 99%

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

Nobukawa¹,

Doho

Shibata³

et al. 2020

IEICE Trans. Fundamentals

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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.

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Section: Fundamental Description Of Rro Feedback Methods In Discrete Mapmentioning

confidence: 99%

Section: Fundamental Description Of Rro Feedback Methods In Discrete Mapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Nobukawa¹,

Doho

Shibata³

et al. 2020

IEICE Trans. Fundamentals

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Controlling Chaotic Resonance using External Feedback Signals in Neural Systems

Nobukawa

Shibata

2019

Sci Rep

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Stochastic resonance is a phenomenon in which the signal response of a non-linear system is enhanced by appropriate external noise. Likewise, a similar phenomenon can be caused by deterministic chaos; this is called chaotic resonance. Devices that employ stochastic resonance have been proposed for the purpose of enhancing tactile sensitivity. However, no applications of chaotic resonance have been reported so far, even though chaotic resonance exhibits a higher sensitivity than stochastic resonance. This contrast in applications could be attributed to the fact that chaotic resonance is induced by adjusting internal parameters. In many cases, especially in biological systems, these parameters are difficult to adjust. In this study, by applying our proposed reduced region of orbit method to a neural system consisting of excitatory and inhibitory neurons, we induce chaotic resonance with signal frequency dependency against weak input signals. Furthermore, the external noise exhibits effects for both diminishing and enhancing signal responses in chaotic resonance. The outcome of this study might facilitate the development of devices utilising the mechanism of chaotic resonance.

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Resonance phenomena controlled by external feedback signals and additive noise in neural systems

Nobukawa

Shibata

Nishimura

et al. 2019

Sci Rep

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Chaotic resonance is a phenomenon that can replace the fluctuation source in stochastic resonance from additive noise to chaos. We previously developed a method to control the chaotic state for suitably generating chaotic resonance by external feedback even when the external adjustment of chaos is difficult, establishing a method named reduced region of orbit (RRO) feedback. However, a feedback signal was utilized only for dividing the merged attractor. In addition, the signal sensitivity in chaotic resonance induced by feedback signals and that of stochastic resonance by additive noise have not been compared. To merge the separated attractor, we propose a negative strength of the RRO feedback signal in a discrete neural system which is composed of excitatory and inhibitory neurons. We evaluate the features of chaotic resonance and compare it to stochastic resonance. The RRO feedback signal with negative strength can merge the separated attractor and induce chaotic resonance. We also confirm that additive noise induces stochastic resonance through attractor merging. The comparison of these resonance modalities verifies that chaotic resonance provides more applicability than stochastic resonance given its capability to handle attractor separation and merging.

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Controlling Chaotic Resonance in Systems with Chaos-Chaos Intermittency Using External Feedback

Cited by 22 publications

References 39 publications

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

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

Controlling Chaotic Resonance using External Feedback Signals in Neural Systems

Resonance phenomena controlled by external feedback signals and additive noise in neural systems

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