Lévy noise induced transitions and enhanced stability in a birhythmic van der Pol system

Yonkeu, R. Mbakob; Yamapi, R.; Филатрелла, Г.; Kurths, Jürgen

doi:10.1140/epjb/e2019-100029-x

Cited by 11 publications

(2 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stochastic effects in birhythmic van der Pol-like model were studied in [44][45][46] with the help of the phase-amplitude approximation and Fokker-Planck equation. This model with Levý noise has been studied in [47]. The effects of uncorrelated white noise on birhythmic hysteretic Josephson junctions were investigated in [48].…”

Section: Introductionmentioning

confidence: 99%

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Bashkirtseva¹,

Ryashko²,

Zaitseva

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

A mathematical model of the biochemical reaction with nonlinear recycling of the product into substrate is considered. The main control parameter of this model is the substrate injection rate, which is subject to random disturbances. We study noise-induced oscillations in the parameter zones where the system is bistable and exhibit a coexistence of the equilibrium and limit cycle, or two stable cycles (birhythmicity). Phenomena of the generation of noisy birhythmicity and 'stochastic preference' of attractors are studied on the basis of the stochastic sensitivity function technique, confidence domains method, and statistics of interspike intervals.

show abstract

Section: Introductionmentioning

confidence: 99%

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Bashkirtseva¹,

Ryashko²,

Zaitseva

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…For additive noise, it has been shown that Lévy flights in a quartic or steeper potential possess finite mean and variance, for all parameters of the Lévy noise [63]. Many classical problems which are well studied for Gaussian noise have been revisited using Lévy noise, such as the escape from a potential well [74][75][76][77][78], noise-induced transitions and stochastic resonance [79][80][81][82][83], oscillators under the influence of noise [62,84,85], the Verhulst model [86] and the Lévy rachet [87]. However, despite this impressive body of work, while the impact of colored noise [23,[88][89][90][91][92] and higher dimensions [93] on on-off intermittency have received attention, the theory of on-off intermittency due to multiplicative Lévy noise close to an instability threshold has not been studied systematically before, to the best of our knowledge.…”

mentioning

confidence: 99%

Lévy on-off intermittency

van Kan,

Alexakis,

Brachet

2021

Preprint

View full text Add to dashboard Cite

We present a new form of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space (α, β) of the noise, with stability parameter α ∈ (0, 2) and skewness parameter β ∈ [−1, 1]. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case α = 2. Three regimes are located at 1 < α < 2, where the noise has finite mean but infinite variance. They are differentiated by β and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterised by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at 0 < α ≤ 1. There, the mean of the noise diverges, and no critical transition occurs. In one case the origin is always unstable, independently of the distance µ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of µ. We thus demonstrate that an instability subject to non-equilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.

show abstract

Bifurcation analysis in the system with the existence of three stable limit cycles

Yuan,

Ning,

Guo

2023

Indian J Phys

View full text Add to dashboard Cite

Lévy noise induced transitions and enhanced stability in a birhythmic van der Pol system

Cited by 11 publications

References 63 publications

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Lévy on-off intermittency

Bifurcation analysis in the system with the existence of three stable limit cycles

Contact Info

Product

Resources

About