Chaotic resonance: Two-state model with chaos-induced escape over potential barrier

Chew, Lock Yue; Ting, Christopher; Lai, Choy Heng

doi:10.1103/physreve.72.036222

Cited by 22 publications

(19 citation statements)

References 49 publications

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“…There is no loss of generality in this choice as chaotic noise from higher even-order Tchebyscheff maps should produce similar results on directed transport as those produced by the secondorder Tchebyscheff map, albeit with a smaller current due to a smaller statistical asymmetric effect. On the other hand, we expect the results for the odd-order Tchebyscheff maps to be the same as those obtained from the Gaussian noise, since all the odd higher-order correlations vanish for both kinds of noise [28,36].…”

Section: Discussionmentioning

confidence: 57%

“…We have also extended the map by incorporating a space-dependent force field on the Brownian particle [28]. This extension has allowed us to examine the mechanism of chaotic transport and chaos-induced escape over potential barriers [36]. It has led us to investigate ratchets driven by chaotic noise both numerically and analytically.…”

Section: Introductionmentioning

confidence: 99%

“…In summary, the research in this paper has gone beyond our earlier work [28,35,36] by providing a systematic treatment on the effects of asymmetry in the potential on directed transport through various configurations of deterministic Smoluchowski-Feynman ratchets driven by chaotic noise. In particular, we have derived a Smoluchowski equation with a source term [Eq.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise

Chew

2012

Phys. Rev. E

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We have elucidated the effect of statistical asymmetry on the directed current in Smoluchowski-Feynman ratchets driven by chaotic noise. Based on the inhomogeneous Smoluchowski equation and its generalized version, we arrive at analytical expressions of the directed current that includes a source term. The source term indicates that statistical asymmetry can drive the system further away from thermodynamic equilibrium, as exemplified by the constant flashing, the state-dependent, and the tilted deterministic Smoluchowski-Feynman ratchets, with the consequence of an enhancement in the directed current.

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Section: Discussionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise

Chew

2012

Phys. Rev. E

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“…In the phenomenon of stochastic resonance [2], for instance, it is the noise intensity that is the parameter in question and only in special cases [3] is there also any matching of frequencies. Recent research has proven that many different kinds of external force can also induce resonances and that the latter can manifest in diverse forms, such as chaotic resonance [4][5][6], stochastic resonance [2,7], coherence resonance [8,9], ghost resonance [10], parametric resonance [1], vibrational resonance [11], anti-resonance [12] and autoresonance [1].…”

Section: Introductionmentioning

confidence: 99%

Vibrational resonance in an oscillator with an asymmetrical deformable potential

et al. 2018

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We report the occurrence of vibrational resonance (VR) for a particle placed in a nonlinear asymmetrical Remoissenet-Peyrard potential substrate whose shape is subjected to deformation. We focus on the possible influence of deformation on the occurrence of vibrational resonance (VR) and show evidence of deformation-induced double resonances. By an approximate method involving direct separation of the timescales, we derive the equation of slow motion and obtain the response amplitude. We validate the theoretical results by numerical simulation. Besides revealing the existence of deformation-induced VR, our results show that the parameters of the deformed potential have a significant effect on the VR and can be employed to either suppress or modulate the resonance peaks, thereby controlling the resonances. By exploring the time series, the phase space structures, and the bifurcation of the attractors in Poincaré section, we demonstrate that there are two distinct dynamical mechanisms that can give rise to deformation-induced resonances, viz: (i) monotonic increase in the size of a periodic orbit; and (ii) bifurcation from a periodic to a quasiperiodic attractor.

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“…Indeed, biological systems effectively utilize the noise generated by their own dynamics to invoke SR, and this mechanism has previously been investigated [18,19]. Among such SR driven by self-generated noises, chaotic resonance (CR) has been spotlighted in the literature [20][21][22][23][24]. CR is a phenomenon in which internal fluctuations are effectively used to trigger state transitions; therefore, CR does not require external noise.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Resonance in Forced Chua^|^apos;s Oscillators

Ishimura

Asai

Motomura

2013

Journal of Signal Processing

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Stochastic resonance (SR) is a phenomenon in which dynamic noise is effectively used to induce state transitions in a double-well potential system driven by subthreshold input signals. The noises are supplied to the system as an additional force. Recently, a phenomenon called "chaotic resonance" (CR) has been spotlighted in the literature. CR can be observed in chaotic systems that have multiple strange attractors and the ability to accept subthreshold input signals; i.e., such CR systems do not require any external noise source, unlike traditional SR systems. In this study, we employed Chua's oscillator as a candidate CR system. The oscillator was driven by a sinusoidal voltage source providing subthreshold input signals. In a certain range of input signal frequencies, we observed chaotic state transitions between the two attractors, whereas no state transition between the attractors was observed in the remaining frequency range. These findings indicated that chaotic fluctuations assisted the state transition. Furthermore, we observed nonmonotonic CR characteristics (correlation value and signal-to-noise ratio between the input signal and the output signal) that corresponded to typical nonmonotonic SR curves.

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Chaotic resonance: Two-state model with chaos-induced escape over potential barrier

Cited by 22 publications

References 49 publications

Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise

Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise

Vibrational resonance in an oscillator with an asymmetrical deformable potential

Chaotic Resonance in Forced Chua^|^apos;s Oscillators

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