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Slowing down critical transitions via Gaussian white noise and periodic force

Science China(Technological Sciences) 2019年第12期62卷 2144-2152页

作者： MA JinZhong XU Yong XU Wei LI YongGe KURTHS Jirge Department of Applied Mathematics Northwestern Polytechnical UniversityXi'an 710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversiyXi'an 710072China Center for Mathematical Sciences&School of Mathematics and Statistics Huazhong University of Science and TechmologyWuhan 430074China Potsdam Institute for Climate Impact Research Potsdam 14412Germany Department of Physics Humboldt UniversityBerlin 12489Germany

Stochastic perturbations and periodic excitations are generally regarded as sources to induce critical transitions in complex systems. However, we find that they are also able to slow down an imminent critical transition. To illustrate this phenomenon, a periodically driven bistable eutrophication model with Gaussian white noise is introduced as a prototype class of real *** residence probability(RP) is presented to measure the possibility that the given system stays in the oligotrophic state versus Gaussian white noise and periodic force. Variations in the mean first passage time(MFPT) and the mean velocity(MV) of the first right-crossing process are also calculated respectively. We show that the frequency of the periodic force can increase the MFPT while reduce the MV under different control parameters. Nevertheless, the noise intensity or the amplitude may result in an increase of the RP only in the case of control parameters approaching the critical values. Furthermore, for an impending critical transition, an increase of the RP appears with the interaction between the amplitude and noise intensity or the combination of the noise intensity and frequency, while the interaction of the frequency and amplitude leads to an extension of the MFPT or a decrease of the MV. As a result, an increase of the RP and MFPT, and a decrease of the MVobtained from our results claim that it is possible to slow down an imminent critical transition via Gaussian white noise and periodic force.

关键词： critical transition slowing down bistable eutrophication model Gaussian white noise periodic force residence probability mean first passage time mean velocity

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CONVERGENCE on A SYMMETRIC ACCELERATED STOCHASTIC ADMM with LARGER STEPSIZES

arXiv

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arXiv 2021年

作者： Bai, Jianchao Han, Deren Sun, Hao Zhang, Hongchao School of Mathematics and Statistics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710129 China LMIB of the Ministry of Education School of Mathematical Sciences Beihang University Beijing100191 China School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710129 China Department of Mathematics Louisiana State University Baton RougeLA70803-4918 United States

In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly nonsmooth convex function and an average function of many smooth convex functions. Our proposed algorithm combines both ideas of ADMM and the techniques of accelerated stochastic gradient methods possibly with variance reduction to solve the smooth subproblem. One main feature of SAS-ADMM is that its dual variable is symmetrically updated after each update of the separated primal variable, which would allow a more flexible and larger convergence region of the dual variable compared with that of standard deterministic or stochastic ADMM. This new stochastic optimization algorithm is shown to have ergodic converge in expectation with O(1/T) convergence rate, where T is the number of outer iterations. Our preliminary experiments indicate the proposed algorithm is very effective for solving separable optimization problems from big-data applications. Finally, 3-block extensions of the algorithm and its variant of an accelerated stochastic augmented Lagrangian method are discussed in the appendix. © 2021, CC BY.

关键词： Convex optimization

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Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes

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Physical Review E 2020年第6期102卷 062106-062106页

作者： Yong Xu Xuemei Liu Yongge Li Ralf Metzler School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan 430074 China Institute for Physics and Astronomy University of Potsdam 14476 Potsdam-Golm Germany

Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent α. In this work we consider a spatially random scenario: in periodic intervals (“layers”) in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent α is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains (“layer thickness”) of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.

关键词： Anomalous diffusion Noise Stochastic processes Random & disordered media Ergodic theory

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Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

arXiv

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arXiv 2020年

作者： Zhang, Xiaoyu Xu, Yong Liu, Qi Kurths, Jürgen Department of Applied Mathematics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xian710072 China Potsdam Institute for Climate Impact Research Potsdam14412 Germany

Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs. When the parameter varies within a certain time scale, the rate will affect the tipping behaviors. These behaviors are undesirable in thermoacoustic systems, which are widely used in aviation, power generation and other industries. Thus, this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises. Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method. Then, the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions. Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption, which is called as a rate-dependent tipping-delay phenomenon. Besides, the influences of the initial values, the rate, the changing time of the parameters, and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail. These results are of great significance for research in related fields such as aviation and land gas turbines. Copyright © 2020, The Authors. All rights reserved.

关键词： White noise

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Rate-dependent bifurcation dodging in a thermoacoustic system driven by colored noise

arXiv

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arXiv 2020年

作者： Zhang, Xiaoyu Xu, Yong Liu, Qi Kurths, Jürgen Grebogi, Celso School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xian710072 China Potsdam Institute for Climate Impact Research Potsdam14412 Germany Institute for Complex Systems and Mathematical Biology School of Natural and Computing Sciences Kings College University of Aberdeen AberdeenAB24 3UE United Kingdom

Tipping in multistable systems occurs usually by varying the input slightly, resulting in the output switching to an often unsatisfactory state. This phenomenon is manifested in thermoacoustic systems. This thermoacoustic instability may lead to the disintegration of rocket engines, gas turbines and aeroengines, so it is necessary to design control measures for its suppression. It was speculated that such unwanted instability states may be dodged by changing quickly enough the bifurcation parameters. Thus, in this work, based on a fundamental mathematical model of thermoacoustic systems driven by colored noise, the corresponding Fokker-Planck-Kolmogorov equation of the amplitude is derived by using a stochastic averaging method. A transient dynamical behavior is identified through a probability density analysis. We find that the rate of change of parameters and the correlation time of the noise are helpful to dodge thermoacoustic instability, while a relatively large noise intensity is a disadvantageous factor. In addition, power-law relationships between the maximum amplitude and the noise parameters are explored, and the probability of successfully dodging a thermoacoustic instability is calculated. These results serve as a guide to the design of engines and to propose an effective control strategy, which is of great significance to aerospace-related fields. Copyright © 2020, The Authors. All rights reserved.

关键词： White noise

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An inexact accelerated stochastic ADMM for separable convex optimization

arXiv

引用

arXiv 2020年

作者： Bai, Jianchao Hager, William W. Zhang, Hongchao School of Mathematics and Statistics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China Department of Mathematics University of Florida PO Box 118105 GainesvilleFL32611-8105 United States Department of Mathematics Louisiana State University Baton RougeLA70803-4918 United States

An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a possibly nonsmooth convex function and a smooth function which is an average of many component convex functions. Problems having this structure often arise in machine learning and data mining applications. AS-ADMM combines the ideas of both ADMM and the stochastic gradient methods using variance reduction techniques. One of the ADMM subproblems employs a linearization technique while a similar linearization could be introduced for the other subproblem. For a specified choice of the algorithm parameters, it is shown that the objective error and the constraint violation are O(1/k) relative to the number of outer iterations k. Under a strong convexity assumption, the expected iterate error converges to zero linearly. A linearized variant of AS-ADMM and incremental sampling strategies are also discussed. Numerical experiments with both stochastic and deterministic ADMM algorithms show that AS-ADMM can be particularly effective for structured optimization arising in big data applications. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

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Chaos and chaos control in MEMS resonators under power law noise

arXiv

引用

arXiv 2019年

作者： Wang, Yunfang Lei, Youming Department of Applied Mathematics Northwestern Polytechnical University Xi'an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an710072 China

The chaotic dynamics and its control under power law noise in Micro-electromechanical systems (MEMS) resonators with electrostatic excitation are probed. On the basis of the stochastic Melnikov method in the mean-square sense and the mean largest Lyapunov exponent, the threshold value of power law noise intensity for the onset of chaos is obtained analytically and numerically. We show that the threshold of noise intensity decreases with the increasing of the frequency exponent of power law noise in the parameter space. Numerical simulations, such as phase diagram and time history, are employed to verify the results acquired by the stochastic Melnikov method. Inspired by the analytical results, a time-delay feedback control algorithm is proposed for controlling the chaotic motion in the resonators. The effectiveness of this controller is certificated by the above numerical method. Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

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Constrained Gaussian process learning for model predictive control

arXiv

引用

arXiv 2019年

作者： Matschek, Janine Himmel, Andreas Sundmacher, Kai Findeisen, Rolf Laboratory for Systems Theory and Automatic Control Otto-von-Guericke University Magdeburg Germany Process Systems Engineering Otto-von-Guericke University Magdeburg Germany Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

Many control tasks can be formulated as a tracking problem of a known or unknown reference signal. Examples are movement compensation in collaborative robotics, the synchronisation of oscillations for power systems or reference tracking of recipes in chemical process operation. Tracking performance as well as guaranteeing stability of the closed loop strongly depends on two factors: Firstly, it depends on whether the future desired tracking reference signal is known and, secondly, whether the system can track the reference at all. This paper shows how to use machine learning, i.e. Gaussian processes, to learn a reference from (noisy) data, while guaranteeing trackability of the modified desired reference predictions in the framework of model predictive control. Guarantees are provided by adjusting the hyperparameters via a constrained optimization. Two specific scenarios, i.e. asymptotically constant and periodical references, are discussed. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution

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Correction: COVID-19 Vaccine Tweets After Vaccine Rollout: Sentiment-Based Topic Modeling

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Journal of medical Internet research 2022年第3期24卷 e37841页

作者： Luwen Huangfu Yiwen Mo Peijie Zhang Daniel Dajun Zeng Saike He Fowler College of Business San Diego State University San Diego CA United States. Center for Human Dynamics in the Mobile Age San Diego State University San Diego CA United States. The State Key Laboratory of Management and Control for Complex Systems Institute of Automation Chinese Academy of Sciences Beijing China. University of Chinese Academy of Sciences Beijing China.

[This corrects the article DOI: 10.2196/31726.].

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Transport and escape in a deformable channel driven by fractional Gaussian noise

引用

Physical Review E 2019年第2期100卷 022114-022114页

作者： Ruoxing Mei Yong Xu Jürgen Kurths Department of Applied Mathematics Northwestern Polytechnical University Xi'an 710072 China Department of Applied Mathematics Northwestern Polytechnical University Xi'an 710072 China and MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China Potsdam Institute for Climate Impact Research Potsdam 14412 Germany

Fractional Gaussian noise (FGN) with the Hurst exponent H is an important tool to model various phenomena in biophysical systems, like subdiffusion in a single protein molecule. Considering that there also exists a confined structure which can be modeled as a channel in these systems, transport and escape driven by FGN in a deformable channel are investigated in this paper. By calculating the mean velocity, and the mean first passage time (MFPT) for crossing the nearest bottleneck and the probability distribution of the final position, effects of FGN and channel structure on the system dynamics are illustrated. Our results indicate that FGN has a complex influence mechanism under different combinations of H and the noise intensity. For a persistence case (H>0.5), the mean velocity decreases but MFPT increases with the increase of the noise intensity and H. While for an antipersistence case (H<0.5), when H is small, the relationships among the mean velocity, MFPT and the noise intensity are exactly the opposite to persistence cases. When H has a large value, the mean velocity tends to first decrease and then increase. Moreover, effects of the bottleneck and channel asymmetry are investigated. It is shown that a small H and a large channel width can lead to a large mean velocity and fast crossing. Besides, a channel asymmetry can affect the system dynamics by inducing asymmetric structure and adjusting the width of bottleneck. However, the effect of the bottleneck is the main factor. Therefore, a combination of channel with wide bottleneck and FGN in an antipersistence regime is the optimal choice to promote the transport and escape. These results provide a basis for the explanation of molecular activity in living organisms and the design of particle mixture separators.

关键词： Noise Particle phenomena Transport phenomena

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