检索结果-内蒙古大学图书馆

Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients

学校读者我要写书评

暂无评论

arXiv 2020年

This work concerned with a non-autonomous slow-fast system, which is generalized by stochastic differential equations (SDEs) with locally Lipschitz coefficients, subjected to standard Brownian motion (Bm) and fraction... 详细信息

关键词： Brownian movement

Chaos and chaos control in MEMS resonators under power law noise

学校读者我要写书评

暂无评论

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

Stability for acoustic wave motion with random force on the locally reacting boundary

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Jiao, Zhe Xu, Yong School of Mathematics and Statistics Northwestern Polytechnical University Xi'An710129 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'An710072 China

This paper concerns about the stability for the acoustic wave motion with boundary frictions and random forces. We will show there exists a unique invariant measure for the stochastic evolution equation associated with this acoustic wave motion, and the invariant measure possesses the property of strong mixing. This result is new with respect to the literature on two accounts: (i) stochasticity is accounted for in the acoustic wave model;(ii) the controllability of the dynamical system modeling the acoustic wave motion implies the *** Codes 60H15, 60G10, 35L52, 35R60 Copyright © 2022, The Authors. All rights reserved.

关键词： Acoustic waves

The central limit theorem for slow-fast systems with Lévy noise

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Yang, Xiaoyu Xu, Yong Wang, Ruifang Jiao, Zhe Department of Mathematics and Statistics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China

We consider a slow-fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the *** Codes 70K70, 60G51, 60G46 Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Precise Laplace approximation for mixed rough differential equation

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Yang, Xiaoyu Xu, Yong Pei, Bin School of Mathematics and Statistics Northwestern Polytechnical University Xi'An710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'An710072 China

This work focuses on the Laplace approximation for the rough differential equation (RDE) driven by mixed rough path (BH, W) with H ∈ (1/3, 1/2) as Ε → 0. Firstly, based on geometric rough path lifted from mixed fractional Brownian motion (fBm), the Schilder-type large deviation principle (LDP) for the law of the first level path of the solution to the RDE is given. Due to the particularity of mixed rough path, the main difficulty in carrying out the Laplace approximation is to prove the Hilbert-Schmidt property for the Hessian matrix of the Itô map restricted on the Cameron-Martin space of the mixed fBm. To this end, we imbed the Cameron-Martin space into a larger Hilbert space, then the Hessian is computable. Subsequently, the probability representation for the Hessian is shown. Finally, the Laplace approximation is constructed, which asserts the more precise asymptotics in the exponential *** Codes 60F10, 60G22, 60H10 Copyright © 2022, The Authors. All rights reserved.

关键词： Laplace transforms

Stability for nonlinear wave motions damped by time-dependent frictions

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Jiao, Zhe Xu, Yong Zhao, Lijing Department of Applied Mathematics Northwestern Polytechnical University Xi’an710129 China MIIT key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China

We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any bifurcation and chaos. And it is a sharp condition on the damping coefficient for the solution to converge to some equilibrium. To illustrate our theoretical results, we provide some numerical simulations for dissipative sine-Gordon equation and dissipative Klein-Gordon *** Codes 35L70, 35B35 Copyright © 2022, The Authors. All rights reserved.

关键词： Damping

A hybrid model based on deep LSTM for predicting high-dimensional chaotic systems

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Lei, Youming Hu, Jian Ding, Jianpeng School of mathematics and statistics Northwestern Polytechnical University Xi'an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an710072 China

We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems. The deep hierarchy is encoded into the LSTM by superimposing multiple recurrent neural network layers and the hybrid model is trained with the Adam optimization algorithm. The statistical results of the Mackey-Glass system and the Kuramoto-Sivashinsky system are obtained under the criteria of root mean square error (RMSE) and anomaly correlation coefficient (ACC) using the singe-layer LSTM, the multi-layer LSTM, and the corresponding hybrid method, respectively. The numerical results show that the proposed method can effectively avoid the rapid divergence of the multi-layer LSTM model when reconstructing chaotic attractors, and demonstrate the feasibility of the combination of deep learning based on the gradient descent method and the empirical model. Copyright © 2020, The Authors. All rights reserved.

关键词： Long short-term memory

Averaging principle of stochastic Burgers equation driven by Lévy processes

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Yue, Hongge Xu, Yong Wang, Ruifang Jiao, Zhe School of Mathematics and Stochastics Northwestern Polytechnical University Xi'an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an710072 China

We are concerned about the averaging principle for the stochastic Burgers equation with slow-fast time scale. This slow-fast system is driven by Lévy processes. Under some appropriate conditions, we show that the slow component of this system strongly converges to a limit, which is characterized by the solution of stochastic Burgers equation whose coefficients are averaged with respect to the stationary measure of the fast-varying jump-diffusion. To illustrate our theoretical result, we provide some numerical *** Codes 60H15, 70K65, 70K70, 34G20 Copyright © 2021, The Authors. All rights reserved.

关键词： Stochastic systems

Elastic Wave Propagation in Nonlinear Two-dimensional Acoustic Metamaterials

学校读者我要写书评

暂无评论

Research Square

Research Square 2021年

作者： Zhao, Cheng Zhang, Kai Zhao, Pengcheng Deng, Zichen School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China

This study describes the wave propagation in a periodic lattice which is formed by a spring-mass two-dimensional structure with local Duffing nonlinear resonators. The wave propagation characteristics of the system is evaluated by using the perturbation method and Floquet-Bloch theorem to determine the dispersion relationships and wave propagation characteristics in the nonlinear two-dimensional acoustic metamaterials (2D AM). A quantitative study of wave amplitude is carried out to reveal the limits of the proposed method. In particular, the harmonic balance method is introduced to investigate the frequency response and effective mass of the nonlinear systems. We find that the dispersion relations, group velocity, negative effective mass of unit-cell are related to wave amplitude. Furthermore, the dual wave vector, bifurcation of periodic solutions and chaotic band are observed in the nonlinear systems. The results can be used to tune wave propagation in the nonlinear acoustic metamaterials and provide some ideas for the study of nonlinear metamaterials. © 2021, CC BY.

关键词： Frequency response