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Path integral solutions for n-dimensional stochastic differential equations underα-stable Lévy excitation

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Theoretical & Applied Mechanics Letters 2023年第2期13卷 98-112页

作者： Wanrong Zan Yong Xu jürgen kurths School of Mathematics Northwest UniversityXi’an710127China Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an710129China MIIT key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an710129China Potsdam Institute for Climate Impact Research Potsdam14412Germany Department of Physics Humboldt University of BerlinBerlin12489Germany

In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and ***,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic ***,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov ***,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

关键词： Path integral method α-stable Lévy noise Monte carlo method Fokker-Planck-Kolmogorov equation

Nonsingularity of Grain-like cascade FSRs via semi-tensor product

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Science China(Information Sciences) 2018年第1期61卷 58-69页

作者： jianquan LU Meilin LI Yang LIU Daniel W.C.HO jrgen kurths School of Mathematics Southeast University College of Mathematics Physics and Information Engineering Zhejiang Normal University Department of Mathematics City University of Hong Kong Potsdam Institute for Climate Impact Research

In this paper, Grain-like cascade feedback shift registers(FSRs) are regarded as two Boolean networks(BNs), and the semi-tensor product(STP) of the matrices is used to convert the Grain-like cascade FSRs into an equivalent linear equation. Based on the STP, a novel method is proposed herein to investigate the nonsingularity of Grain-like cascade FSRs. First, we investigate the property of the state transition matrix of Grain-like cascade FSRs. We then propose their sufficient and necessary nonsingularity condition. Next,we regard the Grain-like cascade FSRs as Boolean control networks(BCNs) and further provide a sufficient condition of their nonsingularity. Finally, two examples are provided to illustrate the results obtained in this paper.

关键词： Grain-like cascade FSRs Boolean control networks Boolean networks semi-tensor product nonsingularity

Cooperative and Competitive Multi-Agent Systems:From Optimization to Games

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IEEE/CAA journal of Automatica Sinica 2022年第5期9卷 763-783页

作者： jianrui Wang Yitian Hong jiali Wang jiapeng Xu Yang Tang Qing-Long Han jürgen kurths Key Laboratory of Smart Manufacturing in Energy Chemical Process Ministry of EducationEast China University of Science and TechnologyShanghai 200237China Department of Electrical and Computer Engineering University of WindsorWindsorON N9B 3P4Canada IEEE School of Science Computing and Engineering TechnologiesSwinburne University of TechnologyMelbourneVIC 3122Australia Potsdam Institute for Climate Impact Research 14473 Potsdam Institute of Physics Humboldt University of Berlin12489 BerlinGermany

Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation *** a multi-agent system,agents with a certain degree of autonomy generate complex interactions due to the correlation and coordination,which is manifested as cooperative/competitive *** survey focuses on multi-agent cooperative optimization and cooperative/non-cooperative *** from cooperative optimization,the studies on distributed optimization and federated optimization are *** survey mainly focuses on distributed online optimization and its application in privacy protection,and overviews federated optimization from the perspective of privacy protection ***,cooperative games and non-cooperative games are introduced to expand the cooperative optimization problems from two aspects of minimizing global costs and minimizing individual costs,***-agent cooperative and non-cooperative behaviors are modeled by games from both static and dynamic aspects,according to whether each player can make decisions based on the information of other ***,future directions for cooperative optimization,cooperative/non-cooperative games,and their applications are discussed.

关键词： Cooperative games counterfactual regret minimization distributed optimization federated optimization fictitious

Fixed-interval smoothing of an aeroelastic airfoil model with cubic or free-play nonlinearity in incompressible flow

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Acta Mechanica Sinica 2021年第7期37卷 1168-1182,I0003页

作者： Qi Liu Yong Xu Yongge Li jurgen kurths Xiaochuan Liu School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an 710072China Potsdam Institute for Climate Impact Research Potsdam 14473Germany Lobachevsky University of Nizhny Novgorod Nizhnij NovgorodRussia AVIC Aircraft Strength Research Institute Xi’an 710065China

Fixed-interval smoothing,as one of the most important types of state estimation,has been concerned in many practical problems especially in the analysis of flight test ***,the existing sequential filters and smoothers usually cannot deal with nonlinear or high-dimensional systems well.A state-of-the-art technique is employed in this study to explore the fixed-interval smoothing problem of a conceptual two-dimensional airfoil model in incompressible flow from noisy measurement ***,the governing equations of the airfoil model are assumed to be known or only partially known.A single objective optimization problem is constructed with the classical Runge–Kutta scheme,and then estimations of the system states,the measurement noise and even the unknown parameters are obtained simultaneously through minimizing the objective *** and feasibility of the method are examined under several simulated measurement data corrupted by different measurement *** the obtained results indicate that the introduced algorithm is applicable for the airfoil model with cubic or free-play structural nonlinearity and leads to accurate state and parameter ***,it is highly robust to Gaussian white and even more complex heavy-tailed measurement *** should be emphasized that the employed algorithm is still effective to high-dimensional nonlinear aeroelastic systems.

关键词： Airfoil model Incompressible flow State estimation Parameter estimation

Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control

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Frontiers of Information Technology & Electronic Engineering 2020年第2期21卷 268-280页

作者： Nan jIANG Chi HUANG Yao CHEN jürgen kurths School of Economic Information Engineering Southwestern University of Finance and EconomicsChengdu 611130China School of Mathematics Southeast UniversityNanjing 210096China Potsdam Inslxtute for Climate Impact Research Potsdam 14412Germany Department of Phystcs Humboldt-Universitcit zu BerlinBerlin 12489Germany Samtov State University Saratov 410012Russia

This study is concerned with probabilistic Boolean control networks(PBCNs)with state feedback control.A novel definition of bisimilar PBCNs is proposed to lower computational *** understand more on bisimulation relations between PBCNs,we resort to a powerful matrix manipulation called semi-tensor product(STP).Because stabilization of networks is of critical importance,the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be ***,the transient periods(the maximum number of steps to implement stabilization)of two PBCNs are certified to be identical if these two networks are paired with a bisimulation *** results are then extended to the probabilistic Boolean networks.

关键词： Probabilistic Boolean control network Bisimulation Stabilization with probability one State feedback control

Synchronization Between Two Coupled Complex Networks

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Synchronization Between Two Coupled Complex Networks

Data-Driven Discovery of Stochastic Differential Equations

第十一届全国非线性振动学术会议暨第八届全国非线性动力学和运动稳定性学术会议

作者： jürgen kurths Institute of Physics University of Potsdam PF 601553

In this contribution we study synchronization for two unidirectionally coupled *** is a substantial generalization of a lot of recent papers investigating synchronization inside a *** derive analytically a criterion for synchronization of two networks which have the same (inside) topological *** numerical examples are given which fit the theoretical *** addition,numerical calculations for two networks with different topological connections are presented and interesting (de) synchronous phenomena are shown,too.

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Engineering 2022年第10期17卷 244-252页

作者： Yasen Wang Huazhen Fang junyang jin Guijun Ma Xin He Xing Dai Zuogong Yue Cheng Cheng Hai-Tao Zhang Donglin Pu Dongrui Wu Ye Yuan jorge Gonçalves jürgen kurths Han Ding School of Mechanical Science and Engineering Huazhong University of Science and TechnologyWuhan 430074China State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and TechnologyWuhan 430074China Department of Mechanical Engineering University of KansasLawrenceKS 66045USA HUST-Wuxi Research Institute Wuxi 214174China Key Laboratory of Image Processing and Intelligent Control School of Artificial Intelligence and AutomationHuazhong University of Science and TechnologyWuhan 430074China Department of Plant Sciences University of CambridgeCambridge CB23EAUK Luxembourg Centre for Systems Biomedicine University of LuxembourgBelvaux 4367Luxembourg Department of Physics Humboldt University of BerlinBerlin 12489Germany Department of Complexity Science Potsdam Institute for Climate Impact ResearchPotsdam 14473Germany

Stochastic differential equations(SDEs)are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different *** identification of SDEs governing a system is often a challenge because of the inherent strong stochasticity of data and the complexity of the system’s *** practical utility of existing parametric approaches for identifying SDEs is usually limited by insufficient data *** study presents a novel framework for identifying SDEs by leveraging the sparse Bayesian learning(SBL)technique to search for a parsimonious,yet physically necessary representation from the space of candidate basis *** importantly,we use the analytical tractability of SBL to develop an efficient way to formulate the linear regression problem for the discovery of SDEs that requires considerably less time-series *** effectiveness of the proposed framework is demonstrated using real data on stock and oil prices,bearing variation,and wind speed,as well as simulated data on well-known stochastic dynamical systems,including the generalized Wiener process and Langevin *** framework aims to assist specialists in extracting stochastic mathematical models from random phenomena in the natural sciences,economics,and engineering fields for analysis,prediction,and decision making.

关键词： Data-driven method System identification Sparse Bayesian learning Stochastic differential equations Random phenomena

Universality in the Synchronization of Weighted Complex Networks

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Universality in the Synchronization of Weighted Complex Netw...

二维格子耦合的Hodgkin-Huxley神经元网(英文)

第三届全国复杂动态网络学术论坛

作者： jürgen kurths Adilson E．Motter Institute of Physics University of Potsdam PF 60155314415 PotsdamGermany Department of Physics and Astronomy Northwestern University EvanstonIL 60208USA

＜正＞We study synchronization in weighted complex networks and identify the leading parameters controlling synchronization. First we analyze the stability of complete synchronization in networks of identical oscillators based on graph spectrum. We show that the synchronizability of random networks with large enough minimal degrees is universally determined by the heterogeneity of node’s intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Further more, we carry out simulations of the synchronization patterns in the network outside the complete synchronization regime, when the coupling is not strong enough or when the synchronization state is perturbed by noise. We find that the effective synchronization is hierarchically organized, depending on the intensities. Nodes with large intensities form effective synchronization clusters.

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二维格子耦合的Hodgkin-Huxley神经元网(英文)