Transitions induced by bounded noise

Bobryk, Roman V.; Chrzeszczyk, A.

doi:10.1016/j.physa.2005.03.055

Cited by 60 publications

(30 citation statements)

References 18 publications

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“…Similar hierarchies were obtained for other dynamical systems in [28][29][30]. Of course we have to close this hierarchy to evaluate p(t, x, y).…”

Section: Response Probability Density Functionssupporting

confidence: 61%

“…A similar explanation is also valid in the twin-well potential case but in that case one can take into consideration that the walls have different form. We performed extensive numerical computations based on hyperbolic system approach [30] to evaluate the PDF of the oscillator with the Ornstein-Uhlenbeck noise excitation and no reentrance transition was found. We suppose that this is true in general case of Gaussian excitations.…”

Section: Reentrance Transitionsmentioning

confidence: 99%

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Transitions in a Duffing oscillator excited by random noise

Bobryk

Chrzeszczyk

2007

Nonlinear Dyn

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We investigate a Duffing oscillator driven by random noise which is assumed to be a harmonic function of the Wiener process. We show that the correlation time of the noise has a strong effect on the form of the response stationary probability density functions. It represents the so-called reentrance transitions, i.e. for the same noise intensity the probability density function has an identical modality for both the small and the large correlation time but a different modality for the moderate correlation time. The transitions are observed for both the single-well and twin-well potential case. A new approach is used to study the response probability density function. It is based on analysis of hyperbolic systems.

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“…Similar hierarchies were obtained for other dynamical systems in [28][29][30]. Of course we have to close this hierarchy to evaluate p(t, x, y).…”

Section: Response Probability Density Functionssupporting

confidence: 61%

Section: Reentrance Transitionsmentioning

confidence: 99%

Transitions in a Duffing oscillator excited by random noise

Bobryk

Chrzeszczyk

2007

Nonlinear Dyn

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“…As reported previously, CCSW noises of 1 ( ) and 2 ( ) are described by following formulas [16,18,33]:…”

Section: Model and Simulationmentioning

confidence: 96%

Breakup of Spiral Wave and Order‐Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross‐Correlated Sine‐Wiener Noises in a Regular Network of Hodgkin‐Huxley Neurons

et al. 2018

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Spatially uniform cross-correlated sine-Wiener (CCSW) noises are imposed on each Hodgkin-Huxley (HH) neuron in a twodimensional (2D) regular network. Noise-induced spiral wave destruction and order-disorder spatial pattern transition can be observed by adjusting cross-correlation time or cross-correlation intensity of CCSW noises. The sudden change of the curve of synchronization factor and the time series of average membrane voltage F can be used to semiquantitatively assess this spatial pattern transition and spiral wave destruction induced by CCSW noises, respectively. In addition, moderate cross-correlation time and strong cross-correlation intensity of CCSW noises are both detrimental to survival of spiral wave. Comparing with non-crosscorrelated sine-Wiener noises, CCSW noises can destroy organized spiral wave with lesser noise amplitude.

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“…For example, biologically paradoxical results occur in the pharmacokinetics model of antitumor chemotherapy: antitumor drugs have the probability of increasing the number of the tumor cells [37,38]. Moreover, experimental studies in sensory and other biological systems support the necessity of using nonGaussian noises [39][40][41]. More importantly, Gaussian noise is inappropriate to directly mimic the signals with a rapidly fluctuating phase.…”

Section: Introductionmentioning

confidence: 99%

“…Many bounded noise-induced phenomena, such as resonance [46,47], transitions [39,48], and spatial synchronization [42], have been reported. We have also investigated the effect of bounded noise on the formation and instability of spiral waves [35,36].…”

Section: Introductionmentioning

confidence: 99%

Subthreshold Periodic Signal Detection by Bounded Noise‐Induced Resonance in the FitzHugh–Nagumo Neuron

et al. 2018

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Neurons can detect weak target signals from complex background signals through stochastic resonance (SR) and vibrational resonance (VR) mechanisms. However, random phase variation of rapidly fluctuating background signals is generally ignored in classical VR or SR studies. Here, the rapidly fluctuating background signals are modeled by bounded noise with random rapidly fluctuating phase derived from Wiener process. Then, the influences of bounded noise on the weak signal detection are discussed in the FitzHugh-Nagumo (FHN) neuron. Numerical results reveal the occurrence of bounded noise-induced single-and biresonance as well as a transition between them. Randomness in phase can enhance the adaptability of neurons, but at the cost of signal detection performance so that neurons can work in more complex environments with a wider frequency range. More interestingly, bounded noise with appropriate parameters can not only optimize information transmission but also simultaneously reduce energy consumption. Finally, the potential mechanism of bounded noise is explained.

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Transitions induced by bounded noise

Cited by 60 publications

References 18 publications

Transitions in a Duffing oscillator excited by random noise

Transitions in a Duffing oscillator excited by random noise

Breakup of Spiral Wave and Order‐Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross‐Correlated Sine‐Wiener Noises in a Regular Network of Hodgkin‐Huxley Neurons

Subthreshold Periodic Signal Detection by Bounded Noise‐Induced Resonance in the FitzHugh–Nagumo Neuron

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