Slowing down critical transitions via Gaussian white noise and periodic force

Ma, Jinzhong; Xu, Yong; Xu, Wei; Li, Yongge; Kurths, Jürgen

doi:10.1007/s11431-019-9557-2

Cited by 42 publications

(14 citation statements)

References 36 publications

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“…Based on the critical slowing down theory, the lag-1 autocorrelation and the variance become the two most commonly used early warning signals [21]. In addition, effective early warning indicators are also proposed in the N-tipping system by combining the concept of basin stability [22,23]. The study of early warning signals is more difficult in systems where both rate and noise are considered, because the parameters are constantly changing making the signals difficult to identify.…”

Section: Introductionmentioning

confidence: 99%

Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

Zhang

Liu

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Thermoacoustic instability has been an important challenge in the development of highperformance combustion systems, as it can have catastrophic consequences. The process of a sudden change in the dynamical behaviour of a thermoacoustic system from a low to a high amplitude thermoacoustic instability, actually entails as a tipping point phenomenon.It has been found that when rate-dependent parameters are considered, a tipping-delay phenomenon may arise, which helps in the control of undesirable states that give rise to thermoacoustic instabilities. This work aims at understanding rate-dependent tipping dynamics of the thermoacoustic system with both time-varying parameters and a non-Gaussian Lévy noise. The latter better describes the severe operating environment of such systems than simpler types of noise. Through numerical simulations, the tipping dynamical behaviour is analysed by considering the rate-dependent parameters coupled with the main parameters of the Lévy noise, including the stability and skewness indices, and the noise intensity. In addition, we investigate the effectiveness of early warning indicators in rate-dependent systems under Lévy noise excitation, and uncover a relationship between warning measures and the rate of change in the parameters. These results inform and enlighten the development and design of power combustion devices, and also provide researchers and engineers with effective ideas to control thermoacoustic instability and the associated tipping dynamics.

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Section: Introductionmentioning

confidence: 99%

Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

Zhang

Liu

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…N is the number of sample points in each sample satisfying N = 10 7 . ξx,nm and ξy,nm are Gaussian random numbers [52]. After this, a Fourier expansion will be applied to 〈 x ( N Δ t )〉 to obtain the amplitude of its first harmonic item A 1 , and then one can calculate η to discuss SR in the triple cavity.…”

Section: Methods To Characterize the Stochastic Resonance-spectral Amplificationmentioning

confidence: 99%

Characterizing stochastic resonance in a triple cavity

Mei

et al. 2021

Phil. Trans. R. Soc. A.

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Many biological systems possess confined structures, which produce novel influences on the dynamics. Here, stochastic resonance (SR) in a triple cavity that consists of three units and is subjected to noise, periodic force and vertical constance force is studied, by calculating the spectral amplification η numerically. Meanwhile, SR in the given triple cavity and differences from other structures are explored. First, it is found that the cavity parameters can eliminate or regulate the maximum of η and the noise intensity that induces this maximum. Second, compared to a double cavity with similar maximum/minimum widths and distances between two maximum widths as the triple cavity, η in the triple one shows a larger maximum. Next, the conversion of the natural boundary in the pure potential to the reflection boundary in the triple cavity will create the necessity of a vertical force to induce SR and lead to a decrease in the maximum of η . In addition, η monotonically decreases with the increase of the vertical force and frequency of the periodic force, while it presents several trends when increasing the periodic force’s amplitude for different noise intensities. Finally, our studies are extended to the impact of fractional Gaussian noise excitations. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

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“…When analyzing the kinetic properties of the DNA catalytic gate, taking random disturbances into consideration can more clearly describe the reaction process of the DNA system. The random perturbation here mainly considers a standard white noise, that is, Gaussian white noise represented by Brownian motion [36]- [38]. The purpose is to construct and analyze the nature to the solution of the DNA catalytic gate system, and deeply understand and analyze the DNA system.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Periodic Solution of DNA Catalytic Reaction Model With Random Disturbance

Zhang

2021

IEEE Open J. Nanotechnol.

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The realization of molecular logic circuit is inseparable from the design and analysis of catalytic reaction chain, and the DNA catalytic gate plays an important role in it. Discuss the nature of the solution to DNA catalytic reaction system, using Khasminskii's periodicity and Lyapunov analysis methods to obtain the existence of non-trivial positive periodic solutions of the system, and the solution is globally attractive. The existence of the solution indicates that according to the mathematical model established by the DNA catalytic reaction system, the system may reach the expected concentration value of an ideal state and obtain better reaction data, which provides a theoretical basis for the realization of the DNA catalytic gate function. Numerical simulation results show that under the influence of random disturbance and periodic parameters, the solution to the random DNA catalytic reaction system exists and is globally attractive, which also reflects that the DNA catalytic reaction system can reach an ideal reaction state. The solution to the DNA catalytic system with random disturbance will converge on a certain value and oscillate periodically between the solution to the deterministic system.

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Slowing down critical transitions via Gaussian white noise and periodic force

Cited by 42 publications

References 36 publications

Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

Characterizing stochastic resonance in a triple cavity

Analysis of Periodic Solution of DNA Catalytic Reaction Model With Random Disturbance

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