Nonlinear Dynamics of Chaotic and Stochastic Systems

Anishchenko, Vadim Semonovich; Astakhov, V. V.; Neiman, Alexander; Вадивасова, Т. Е.; Schimansky‐Geier, Lutz

doi:10.1007/978-3-540-38168-6

Cited by 86 publications

(37 citation statements)

References 310 publications

(470 reference statements)

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“…We previously reported that these characteristics are maintained under RRO feedback signals in discrete chaotic systems [38], [44], [45]. Therefore, the characteristics of chaotic resonance observed in this study are congruent with the previous findings of [19], [38], [44], [45].…”

Section: Discussionsupporting

confidence: 93%

“…Consequently, this effect enhances the signal response. It is known that, in discrete and continuous chaotic systems with CCI, the signal response in chaotic resonance is also maximized at around the attractor-merging bifurcation, and its response exhibits dependency on the input frequency [19]. We previously reported that these characteristics are maintained under RRO feedback signals in discrete chaotic systems [38], [44], [45].…”

Section: Discussionmentioning

confidence: 92%

“…(2) has two symmetric attractor regions, i.e., positive and negative x(t) regions. Under the condition for no feedback signals (K = 0), by increasing the internal parameter a, the chaotic attractors, which were separated to two symmetric attractor regions, are merged and CCI arises [19]. The conditions for attractor merging are determined by satisfying…”

Section: Fundamental Description Of Rro Feedback Methods In Discrete Mapmentioning

confidence: 99%

“…The former one is called stochastic resonance, which is observed in various kinds of systems, such as climate systems, nonlinear electric circuits, biological systems, and social systems [10]- [17]. The latter one is called chaotic resonance [18], [19], which is observed in systems with chaoschaos intermittency (CCI) where the chaotic orbit appears between separate regions, such as one-dimensional cubic map, Chua's circuit, Lorenz systems, and duffing systems [20], [21] (reviewed in [19], [22]- [24]). In chaotic resonance, switching between different regions in CCI synchronizes with a weak external signal and its degree is maximized near the conditions where an attractor-merging bifurcation arises [19].…”

Section: Introductionmentioning

confidence: 99%

“…The latter one is called chaotic resonance [18], [19], which is observed in systems with chaoschaos intermittency (CCI) where the chaotic orbit appears between separate regions, such as one-dimensional cubic map, Chua's circuit, Lorenz systems, and duffing systems [20], [21] (reviewed in [19], [22]- [24]). In chaotic resonance, switching between different regions in CCI synchronizes with a weak external signal and its degree is maximized near the conditions where an attractor-merging bifurcation arises [19]. Studies on chaotic resonance have been proceeding toward neural systems [18], [21], [25]- [30].…”

Section: Introductionmentioning

confidence: 99%

See 4 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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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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