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Dr. Yong Xu
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Representative Publications
View All Publications26 May 2011 in Physical Review E
Journal Article
YXYong Xu
Yong XuRGRencai Gu
Rencai Gu
HZHuiqing Zhang
Huiqing Zhang
WXWei Xu
Wei Xu
JDJinqiao Duan
Jinqiao Duan
This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing–Van der Pol oscillator. By using the stochastic averaging method, theoretically, one can obtain the stationary probability density function of amplitude for the Duffing–Van der Pol oscillator and can reveal interesting dynamics under the influence of Gaussian colored noise. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that system parameters, noise intensity, and noise correlation time, respectively, can be treated as bifurcation parameters. They also imply that the effects of multiplicative noise are rather different from that of additive noise. The results of direct numerical simulation verify the effectiveness of the theoretical analysis. Moreover, the largest Lyapunov exponent calculations indicate that and bifurcations have no direct connection.
1 August 2011 in Physica D: Nonlinear Phenomena
Journal Article
1 January 2020 in Chaos: An Interdisciplinary Journal of Nonlinear Science
Journal Article
YXYong Xu
Yong XuHZHao Zhang
Hao Zhang
YLYongge Li
Yongge Li
KZKuang Zhou
Kuang Zhou
QLQi Liu
Qi Liu
JKJürgen Kurths
Jürgen KurthsThe probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation. A novel machine learning method is developed to solve the general FP equations based on deep neural networks. The proposed algorithm does not require any interpolation and coordinate transformation, which is different from the traditional numerical methods. The main novelty of this paper is that penalty factors are introduced to overcome the local optimization for the deep learning approach, and the corresponding setting rules are given. Meanwhile, we consider a normalization condition as a supervision condition to effectively avoid that the trial solution is zero. Several numerical examples are presented to illustrate performances of the proposed algorithm, including one-, two-, and three-dimensional systems. All the results suggest that the deep learning is quite feasible and effective to calculate the FP equation. Furthermore, influences of the number of hidden layers, the penalty factors, and the optimization algorithm are discussed in detail. These results indicate that the performances of the machine learning technique can be improved through constructing the neural networks appropriately.
1 October 2014 in Communications in Nonlinear Science and Numerical Simulation
Journal Article
13 January 2016 in Science China Technological Sciences
Journal Article
1 February 2020 in Applied Mathematics Letters
Journal Article
About Me
Yong Xu is a Professor at Northwestern Polytechnical University. His research projects are The NSF of China, Stochastic Nonlinear Dynamics and its Applications in Some Biological Systems with Lévy Noise, (2014.1-2017.12), PI, The NSF of China, (2010.1-2012.12), PI. The NSF of China, The First International Conference on Dynamical Systems and Modern Applied Mathematics, (2011.3-2011.12), PI, Program for New Century Excellent Talents in University, (2012.1-2014.12), PI, The Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, (2012.1-2013.12), PI, Shaanxi Project for Young New Star in Science \& Technology, (2012.1-2014.12), PI.
He a referee for Mathematical Review (reviewer), International Journal of Bifurcation \& Chaos' Nonlinear Dynamics, Journal of Vibration and Control, Applied Mathematics and Computation, Mathematics and Computers in Simulation, Physica A, Advances in Mathematics and Physics' Stochastic \& Dynamics, Applied Mathematical Modelling, Chinese Quarterly Journal of Mathematics, Chinese Journal of Theoretical and Applied Mechanics, Science in China, Theoretical and Applied Mechanics Letters. He has served as Visiting Professor at University of Bielefield, Germany, (2012.1.15-2012.2.13), Friedrich-Schiller-University Jena, Germany, (2012.2.1-2012.2.3). His research interests are Random /Complex Dynamical Systems, Nonlinear/Stochastic Dynamics, Applied Probability & Statistics, and Non-Gaussian noise.