Delay-induced stochastic bifurcations in a bistable system under white noise

Sun, Zhongkui; Fu, Jin; Xiao, Yuzhu; Xu, Wei

doi:10.1063/1.4927646

Cited by 41 publications

(11 citation statements)

References 35 publications

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“…Ashwin et al [33] study the regimes of transition and the escape time in a network of bistable nodes as a function of the coupling and noise strengths. Sun and coworkers [34] assess the possibility of tipping for a Duffing-Van der Pol oscillator with time-delayed feedback, as a function of forcing noise intensity, feedback time delay and feedback intensity. The work from Clements and Ozgul [35] deals with two stochastic models for population dynamics, and studies the effect of the rate of change of one governing parameter on the system dynamics and on the predictability of tipping.…”

Section: Introductionmentioning

confidence: 99%

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

et al. 2018

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Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.

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Section: Introductionmentioning

confidence: 99%

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

et al. 2018

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“…synchronized switching harvesting on inductor and switching controller) have been proposed to solve this critical problem [30,31]. A simple and effective control strategy is time-delayed feedback control, which has been widely used to control bifurcation, chaos, resonance, and birhythmicity [32][33][34][35][36]. In addition, as an important renewable energy source, wind energy has received extensive attention from scholars [2,31].…”

Section: Introductionmentioning

confidence: 99%

Time‐Delayed Feedback Control in the Multiple Attractors Wind‐Induced Vibration Energy Harvesting System

et al. 2019

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This paper proposes a time-delayed feedback control to improve collection performance of the multiple attractors wind-induced vibration energy harvester system. By employing a conversion mechanism for decoupling the electromechanical equations and the stochastic averaging method, the roles of the time-delayed feedback and the system parameters have been systematically examined. In the deterministic case, the time delay can control efficiently the birhythmic properties; thus one can realize a dividing line in the parameter plane that separates the space into two subspaces of generically distinct nature. Further, it is exclusively demonstrated that implementing time-delayed feedback control serves as a very simple but highly efficient scheme to increase the harvested energy from vibrations in presence of noise disturbances. Additionally, the time constant ratio and coupling coefficients can also be properly tuned to optimize power generation.

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“…However, existence of stationary densities for Chua's circuit driven by skew-normal distributed noise is not yet available in the literature. Limit cycles of the Lorenz system driven by the Wiener process have been analyzed by P-bifurcation and D-bifurcation in [11], and the e®ect of time delay on the stochastic bifurcation in Van der Pol oscillator perturbed by white noise have been investigated in [12]. The e®ect of noise on the dynamical systems which have hidden attractors has been investigated in [13], and the analytical and numerical methods for the problem of localization of hidden attractors in Chua's circuit have been developed in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Bifurcation in Generalized Chua’s Circuit Driven by Skew-Normal Distributed Noise

2018

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In this study, the stochastic phenomenological bifurcations (P-bifurcations) of generalized Chua’s circuit (GCC) driven by skew-normal distributed noise have been investigated by numerically obtaining the stationary distributions of the stochastic responses. The noise intensity and/or skewness parameters of skew-normal distributed noise have been chosen as the bifurcation parameters to change the structure of the stochastic attractor. While the number of breakpoints in the piecewise-linear characteristics of the GCC are fixed, it has been observed that the number of scrolls have been changed by tuning the noise intensity and the skewness parameter of the skew-normal distributed noise.

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Delay-induced stochastic bifurcations in a bistable system under white noise

Cited by 41 publications

References 35 publications

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Time‐Delayed Feedback Control in the Multiple Attractors Wind‐Induced Vibration Energy Harvesting System

Stochastic Bifurcation in Generalized Chua’s Circuit Driven by Skew-Normal Distributed Noise

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