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Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

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Chinese Physics B 2020年第5期29卷 155-164页

作者： Ting-Ting Shi Xue-Mei Xu Ke-Hui Sun Yi-Peng Ding Guo-Wei Huang School of Physics and Electronics Central South UniversityChangsha 410083China

Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored *** analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay *** effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are ***,three types of asymmetric potential function characteristics are thoroughly *** they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),*** conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite ***,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic *** experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.

关键词： asymmetric stochastic resonance time-delayed feedback non-Gaussian colored noise weak signal detection

Control of Halo-Chaos in Beam Transport Network via Neural Network Adaptation with time-delayed feedback

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Communications in Theoretical Physics 2006年第1期45卷 117-120页

作者： FANG Jin-Qing LUO Xiao-Shu Guo-Xian China institute of Atomic Energy P.O. Box 275-27 Beijing 102413 China Department of Physics and Electronic Science Guangxi Normal University Guilin 541004 China

Subject of the halo-chaos control in beam transport networks （channels） has become a key concerned issue for many important applications of high-current proton beam since 1990＇. In this paper, the magnetic field adaptive control based on the neural network with time-delayed feedback is proposed for suppressing beam halo-chaos in the beam transport network with periodic focusing channels. The envelope radius of high-current proton beam is controlled to reach the matched beam radius by suitably selecting the control structure and parameter of the neural network, adjusting the delayed-time and control coefficient of the neural network.

关键词： beam transport network periodic focusing channels high-current proton beam halo-chaos neural network adaptation control time-delayed feedback

BIFURCATION ANALYSIS IN A GENERALIZED FRICTION MODEL WITH time-delayed feedback

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Annals of Differential Equations 2014年第2期30卷 199-215页

作者： Chuang Xu Junjie Wei Dept. of Math. Harbin Institute of Technology Harbin 150001 Dept. of Mathematical and Statistical Sciences University of AlbertaEdmonton Alberta Canada T6G 2G1

In this paper, we consider a generalized model of the two friction models, both of which have two different types of control forces with time-delayed feedback proposed by Ashesh Sara et al. By taking the time delay as the bifurcation parameter, we discuss the local stability of the Hopf bifurcations. Under some condition, the generalized model harbors a phenomenon that the equilibrium may undergo finite switches from stability to instability to stability and finally become unstable. By applying the method introduced by Faria and Magalhaes, we compute the normal form on the center manifold to determine the direction and stability of the Hopf bifurcations. Numerical simulations are carried out and more than one periodic solutions may exist according to the bifurcation diagram given by BIFTOOL. Finally a brief conclusion is presented.

关键词： Hopf bifurcation friction-driven oscillation time-delayed feedback periodic solution complex dynamical behavior

Some stability analysis of a non-linear time-delayed feedback circuit

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Some stability analysis of a non-linear time-delayed feedbac...

An underdamped and delayed tri-stable model-based stochastic resonance

第24届中国控制与决策会议

作者： Shravan Mohan Gaurav Raina the Department of Electrical Engineering Indian Institute of Technology Madras the Faculty of the Department of Electrical Engineering Indian Institute of Technology Madras

A key focus of this paper is on understanding stability in a non-linear circuit design subject to delayed feedback. The system we consider is an autonomous first order RC circuit, coupled with a non-linear element, with a fixed feedback delay. With time delays, stability is a key concern. So for the non-linear circuit model we first establish a sufficient condition for local stability. We then establish necessary and sufficient conditions for local stability. Additionally we also exhibit that when local stability is just lost, a Hopf type bifurcation would occur. For the non-linear system, this bifurcation signifies the emergence of limit cycles which can degrade performance. Practically, it is useful to obtain an estimate of the amplitude and frequency of the bifurcating periodic solutions. Such estimates are calculated using the method of harmonic balance. In addition to the local stability analysis, we also establish some global stability results and some conditions to ensure that the solutions of the governing non-linear system are bounded. Some of the theoretical insights obtained are complemented with numerical simulations and also with experiments which are carried out using off-the-shelf components. The combination of theory, both local and global, simulations and experiments serve to enhance our understanding of the underlying model.

关键词： Non-linear Circuit time-delayed feedback Stability Hopf Bifurcation Experiments.

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Chinese Physics B 2024年第1期33卷 280-286页

作者：靳艳飞王昊天张婷婷 Department of Mechanics Beijing Institute of TechnologyBeijing 100081China

Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.

关键词： stochastic resonance underdamped tri-stable system spectral amplification time-delayed feedback

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

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Chinese Physics B 2010年第4期19卷 90-95页

作者：郭永峰徐伟王亮 Department of Applied Mathematics Northwestern Polytechnical University

This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.

关键词： stochastic resonance time-delayed feedback mixed periodic signal signal-to-noise ratio