Can noise make nonbursting chaotic systems more regular?

Zhu, Liqiang; Lai, Ying–Cheng; Liu, Zonghua; Raghu, Arvind

doi:10.1103/physreve.66.015204

Cited by 14 publications

(3 citation statements)

References 27 publications

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“…One of the most well-known effects of noise is coherence resonance (CR) [2][3][4], by which the oscillatory response of an excitable system is the most coherent state at an optimal noise level. Existence of the coherence resonance has been demonstrated both theoretically and experimentally in different models of single and coupled excitable systems [5][6][7][8][9][10][11], including neuronal systems.…”

Section: Introductionmentioning

confidence: 98%

Enhancement of temporal coherence via time-periodic coupling strength in a scale-free network of stochastic Hodgkin–Huxley neurons

2015

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Section: Introductionmentioning

confidence: 98%

Enhancement of temporal coherence via time-periodic coupling strength in a scale-free network of stochastic Hodgkin–Huxley neurons

2015

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“…These remarkable characteristics mean that the investigation of VR in the canonical Chua's circuit is universal and propagable. Additionally, in non-autonomous Chua's circuit systems, researchers have investigated the mechanism for achieving voltage gain from Chua's circuit using noise or periodic signals, for example, SR [33,34], VR [22,24], and coherence resonance [35,36]. In these reported studies, nonlinear resistors whose voltage-current curve is a linear piecewise functions are employed.…”

Section: Introductionmentioning

confidence: 99%

Vibrational resonance and chaos control in the canonical Chua's circuit with a smooth nonlinear resistor

Li,

Liu,

2024

Preprint

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Vibrational resonance and chaos control in the canonical Chua's circuit with a smooth cubic nonlinear resistoris investigated by an analog circuit experiment and a dynamical model. When other parameters are fixed, changingthe amplitude and the frequency of the high-frequency signal can make the system's response amplitude to thelow-frequency weak signal exists a wide peak. The phase diagram of the system will transition from a single-scrollattractor to a double-scroll attractor when the amplitude of the high-frequency signal reaches the critical valueto achieve vibrational resonance. In particular, the maximum of the system's response amplitude is insusceptiblewhen the frequency of the high-frequency signal varies over a broad range, which indicates the strong robustnessof the vibrational resonance in the present system. The experimental results are coincident with the numericalsimulations. This research has potential applications in chaos control and weak signal detection.

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“…Also intriguing is the SR without an external periodic force, whereby noise alone extracts a hidden intrinsic time scale of the dynamics in a resonant manner. The most commonly used term for the latter phenomenon is coherence resonance or autonomous SR. [16][17][18][19] Aside from these two rather mainstream phenomena, there exist several related reports on noise-induced order either from chaotic states, 20,21 by means of variations in system size 22 and diversity, 23 or via an enhancement of synchronization in coupled systems. [24][25][26] Furthermore, order out of noise has been studied extensively also in nonidentical ensembles governed by nonlinear dynamics, such as neurons, 27 as well as in small-world neuronal networks 28 and bistable overdamped oscillators.…”

Section: Introductionmentioning

confidence: 99%

Spatial Coherence Resonance in Delayed Hodgkin–huxley Neuronal Networks

Wang

Perc

Duan

et al. 2010

Int. J. Mod. Phys. B

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We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instantaneous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might nevertheless preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the fraction of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.

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Can noise make nonbursting chaotic systems more regular?

Cited by 14 publications

References 27 publications

Enhancement of temporal coherence via time-periodic coupling strength in a scale-free network of stochastic Hodgkin–Huxley neurons

Enhancement of temporal coherence via time-periodic coupling strength in a scale-free network of stochastic Hodgkin–Huxley neurons

Vibrational resonance and chaos control in the canonical Chua's circuit with a smooth nonlinear resistor

Spatial Coherence Resonance in Delayed Hodgkin–huxley Neuronal Networks

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