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Computing large deviation prefactors of stochastic dynamical systems based on machine learning
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作者 李扬 袁胜兰 +1 位作者 陆凌宏志 刘先斌 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期364-373,共10页
We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for m... We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations. 展开更多
关键词 machine learning large deviation prefactors stochastic dynamical systems rare events
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A Dynamical System-Based Framework for Dimension Reduction
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作者 Ryeongkyung Yoon Braxton Ostin 《Communications on Applied Mathematics and Computation》 EI 2024年第2期757-789,共33页
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a... We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap. 展开更多
关键词 Dimension reduction Equation discovery dynamical systems Adjoint method Optimal transportation
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Dynamic Constraint-Driven Event-Triggered Control of Strict-Feedback Systems Without Max/Min Values on Irregular Constraints
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作者 Zhuwu Shao Yujuan Wang +1 位作者 Zeqiang Li Yongduan Song 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第3期569-580,共12页
This work proposes an event-triggered adaptive control approach for a class of uncertain nonlinear systems under irregular constraints.Unlike the constraints considered in most existing papers,here the external irregu... This work proposes an event-triggered adaptive control approach for a class of uncertain nonlinear systems under irregular constraints.Unlike the constraints considered in most existing papers,here the external irregular constraints are considered and a constraints switching mechanism(CSM)is introduced to circumvent the difficulties arising from irregular output constraints.Based on the CSM,a new class of generalized barrier functions are constructed,which allows the control results to be independent of the maximum and minimum values(MMVs)of constraints and thus extends the existing results.Finally,we proposed a novel dynamic constraint-driven event-triggered strategy(DCDETS),under which the stress on signal transmission is reduced greatly and no constraints are violated by making a dynamic trade-off among system state,external constraints,and inter-execution intervals.It is proved that the system output is driven to close to the reference trajectory and the semi-global stability is guaranteed under the proposed control scheme,regardless of the external irregular output constraints.Simulation also verifies the effectiveness and benefits of the proposed method. 展开更多
关键词 Adaptive control dynamic constraint-driven event-triggered control irregular output constraints nonlinear strict-feed-back systems
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THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS
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作者 张瑞丰 朱姜慧 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1915-1924,共10页
Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the v... Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy. 展开更多
关键词 packing entropy variational principle nonautonomous dynamical systems
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Numerical Modelling of Ore-forming Dynamics of Fractal Dispersive Fluid Systems 被引量:8
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作者 邓军 方云 +3 位作者 杨立强 杨军臣 孙忠实 王建平 丁式江 王庆飞 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2001年第2期220-332,共13页
Based on an analysis of the fractal structures and mass transport mechanism of typical shear-fluid-ore formation system, the fractal dispersion theory of the fluid system was used in the dynamic study of the ore forma... Based on an analysis of the fractal structures and mass transport mechanism of typical shear-fluid-ore formation system, the fractal dispersion theory of the fluid system was used in the dynamic study of the ore formation system. The model of point-source diffusive illuviation of the shear-fluid-ore formation system was constructed, and the numerical simulation of dynamics of the ore formation system was finished. The result shows that: (1) The metallogenic system have nested fractal structure. Different fractal dimension values in different systems show unbalance and inhomogeneity of ore-forming processes in the geohistory. It is an important parameter to symbolize the process of remobilization and accumulation of ore-forming materials. Also it can indicate the dynamics of the metallogenic system quantitatively to some extent. (2) In essence, the fractal dispersive ore-forming dynamics is a combination of multi-processes dominated by fluid dynamics and supplemented by molecule dispersion in fluids and fluid-rock interaction. It changes components and physico-chemical properties of primary rocks and fluids, favouring deposition and mineralization of ore-forming materials. (3) Gold ore-forming processes in different types of shear zones are quite different. (1) In a metallogenic system with inhomogeneous volumetric change and inhomogeneous shear, mineralization occurs in structural barriers in the centre of a shear zone and in geochemical barriers in the shear zone near its boundaries. But there is little possibility of mineralization out of the shear zone. (2) As to a metallogenic system with inhomogeneous volumetric change and simple shear, mineralization may occur only in structural barriers near the centre of the shear zone. (3) In a metallogenic system with homogeneous volumetric change and inhomogeneous shear, mineralization may occur in geochemical barriers both within and out of the shear zone. 展开更多
关键词 fluid system fractal dispersion point-source illuviation model ore-forming dynamics numerical simulation
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Foundations and Applications of Information Systems Dynamics
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作者 Jianfeng Xu Zhenyu Liu +4 位作者 Shuliang Wang Tao Zheng Yashi Wang Yingfei Wang Yingxu Dang 《Engineering》 SCIE EI CAS CSCD 2023年第8期254-265,共12页
Although numerous advances have been made in information technology in the past decades,there is still a lack of progress in information systems dynamics(ISD),owing to the lack of a mathematical foundation needed to d... Although numerous advances have been made in information technology in the past decades,there is still a lack of progress in information systems dynamics(ISD),owing to the lack of a mathematical foundation needed to describe information and the lack of an analytical framework to evaluate information systems.The value of ISD lies in its ability to guide the design,development,application,and evaluation of largescale information system-of-systems(So Ss),just as mechanical dynamics theories guide mechanical systems engineering.This paper reports on a breakthrough in these fundamental challenges by proposing a framework for information space,improving a mathematical theory for information measurement,and proposing a dynamic configuration model for information systems.In this way,it establishes a basic theoretical framework for ISD.The proposed theoretical methodologies have been successfully applied and verified in the Smart Court So Ss Engineering Project of China and have achieved significant improvements in the quality and efficiency of Chinese court informatization.The proposed ISD provides an innovative paradigm for the analysis,design,development,and evaluation of large-scale complex information systems,such as electronic government and smart cities. 展开更多
关键词 system-of-systems engineering Information theory Information measurement Information systems dynamics Judicial informatization
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Distributed dynamic event-based finite-time dissipative synchronization control for semi-Markov switched fuzzy cyber-physical systems against random packet losses
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作者 伍锡如 张煜翀 +1 位作者 张畑畑 张斌磊 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第10期328-342,共15页
This paper is concerned with the finite-time dissipative synchronization control problem of semi-Markov switched cyber-physical systems in the presence of packet losses, which is constructed by the Takagi–Sugeno fuzz... This paper is concerned with the finite-time dissipative synchronization control problem of semi-Markov switched cyber-physical systems in the presence of packet losses, which is constructed by the Takagi–Sugeno fuzzy model. To save the network communication burden, a distributed dynamic event-triggered mechanism is developed to restrain the information update. Besides, random packet dropouts following the Bernoulli distribution are assumed to occur in sensor to controller channels, where the triggered control input is analyzed via an equivalent method containing a new stochastic variable. By establishing the mode-dependent Lyapunov–Krasovskii functional with augmented terms, the finite-time boundness of the error system limited to strict dissipativity is studied. As a result of the help of an extended reciprocally convex matrix inequality technique, less conservative criteria in terms of linear matrix inequalities are deduced to calculate the desired control gains. Finally, two examples in regard to practical systems are provided to display the effectiveness of the proposed theory. 展开更多
关键词 cyber-physical systems finite-time synchronization distributed dynamic event-triggered mechanism random packet losses
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Einstein-Podolsky-Rosen Steering and Nonlocality in Open Quantum Systems
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作者 Abdelaziz Sabik 《Journal of Modern Physics》 2024年第4期462-473,共12页
We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dyna... We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods. 展开更多
关键词 Quantum Steering dynamical Semigroups Bell Nonlocality Open Quantum system Asymptotic dynamics Entanglement
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Ore-forming Fluid Systems and Mineralization in the Eastern Jiangnan Uplift in the Border Area of Anhui and Jiangxi Provinces, China 被引量:3
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作者 ZHOUTaofa YUANFeng +4 位作者 HOUMingjin FAnYu DUJianguo ZHUGuang YUEShucang 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2004年第2期380-386,共7页
Obvious differences in mineralization characteristics exist between the southern and northern parts of the eastern part of the Jiangnan Uplift in northern Jiangxi Province and southern Anhui Province. The regional met... Obvious differences in mineralization characteristics exist between the southern and northern parts of the eastern part of the Jiangnan Uplift in northern Jiangxi Province and southern Anhui Province. The regional metallogeny is discussed, and the ore-forming fluid systems are classified in this article. It is proposed that the fluid ore-forming activities in the Jiangnan Uplift both in northern Jiangxi and southern Anhui have close relationships with the crust-mantle interaction and magmatic-tectonic activities. The types and scales of the mineralization on the both sides of the eastern Jiangnan Uplift were determined by fluid ore-forming systems and geological backgrounds. 展开更多
关键词 ore-forming fluid systems MINERALIZATION Jiangnan Uplift ANHUI northern Jiangxi
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Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques 被引量:1
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作者 LIU Minzhong KANG Lisha 《Wuhan University Journal of Natural Sciences》 EI CAS 2006年第3期520-524,共5页
We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The conver... We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems (mainly the Lorenz and Chen systems). The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems. 展开更多
关键词 dynamical evolutionary algorithm nonlinear dynamical systems RECONSTRUCTION
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CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS 被引量:1
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作者 黎育红 Zdzistaw Brze■niak 周建中 《Acta Mathematica Scientia》 SCIE CSCD 2008年第2期253-268,共16页
The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on... The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS. 展开更多
关键词 Random dynamical systems asymptotic compactness DISSIPATIVITY Random attractor Sobolev compact embedding
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Controllable Subspaces of Open Quantum Dynamical Systems 被引量:1
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作者 ZHANG Ming DAI Hong-Yi +2 位作者 GONG Er-Ling XIE Hong-Wei HU De-Wen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第1期61-64,共4页
This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perf... This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation. 展开更多
关键词 quantum dynamical systems CONTROLLABILITY decoherence-free subspace
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Comparing dynamical systems concepts and techniques for biomechanical analysis 被引量:3
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作者 Richard E.A.van Emmerik Scott W.Ducharme +1 位作者 Avelino C.Amado Joseph Hamill 《Journal of Sport and Health Science》 SCIE 2016年第1期3-13,共11页
Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predomin... Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints. 展开更多
关键词 Adaptability Complexity dynamical systems Nonlinear dynamics Stability Variability
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Use of Dynamical Systems Modeling to Hybrid Cloud Database 被引量:1
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作者 Evgeniy V. Pluzhnik Evgeny V. Nikulchev 《International Journal of Communications, Network and System Sciences》 2013年第12期505-512,共8页
In the article, an experiment is aimed at clarifying the transfer efficiency of the database in the cloud infrastructure. The system was added to the control unit, which has guided the database search in the local par... In the article, an experiment is aimed at clarifying the transfer efficiency of the database in the cloud infrastructure. The system was added to the control unit, which has guided the database search in the local part or in the cloud. It is shown that the time data acquisition remains unchanged as a result of modification. Suggestions have been made about the use of the theory of dynamic systems to hybrid cloud database. The present work is aimed at attracting the attention of specialists in the field of cloud database to the apparatus control theory. The experiment presented in this article allows the use of the description of the known methods for solving important practical problems. 展开更多
关键词 Hybrid CLOUD DATABASE CLOUD COMPUTING Time of QUERY dynamical systems Control THEORY
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Fault-tolerant finite-time dynamical consensus of double-integrator multi-agent systems with partial agents subject to synchronous self-sensing function failure 被引量:1
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作者 Zhi-Hai Wu Lin-Bo Xie 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第12期719-725,共7页
This paper investigates fault-tolerant finite-time dynamical consensus problems of double-integrator multi-agent systems(MASs)with partial agents subject to synchronous self-sensing function failure(SSFF).A strategy o... This paper investigates fault-tolerant finite-time dynamical consensus problems of double-integrator multi-agent systems(MASs)with partial agents subject to synchronous self-sensing function failure(SSFF).A strategy of recovering the connectivity of network topology among normal agents based on multi-hop communication and a fault-tolerant finitetime dynamical consensus protocol with time-varying gains are proposed to resist synchronous SSFF.It is proved that double-integrator MASs with partial agents subject to synchronous SSFF using the proposed strategy of network topology connectivity recovery and fault-tolerant finite-time dynamical consensus protocol with the proper time-varying gains can achieve finite-time dynamical consensus.Numerical simulations are given to illustrate the effectiveness of the theoretical results. 展开更多
关键词 multi-agent systems synchronous self-sensing function failure finite-time dynamical consensus network topology connectivity recovery
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GLOBAL VIEW OF MICROSTRUCTURAL EVOLUTION:ENERGETICS,KINETICS AND DYNAMICAL SYSTEMS 被引量:4
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作者 杨卫 锁志钢 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1996年第2期144-157,共14页
An evolving material structure is in a non-equilibrium state, with free energy expressed by the generalized coordinates. A global approach leads to robust computations for the generalized thermodynamic forces. Those f... An evolving material structure is in a non-equilibrium state, with free energy expressed by the generalized coordinates. A global approach leads to robust computations for the generalized thermodynamic forces. Those forces drive various kinetic processes, causing dissipation at spots, along curves, surfaces and interfaces, and within volumetric regions. The actual evolution path, and therefore the final equilibrium state, is determined by the energetics and kinetics. A virtual work principle Links the free energy landscape and the kinetic processes, and assigns a viscous environment to every point on the landscape. The approach leads to a dynamical system that governs the evolution of generalized coordinates. The microstructural evolution is globally characterized by a basin map in the coordinate space; and by a diversity map and a variety map in the parameter space. The control of basin boundaries raises the issue of energetic and kinetic bifurcations. The variation of basin boundaries under different sets of controlling parameters provides an analytical way to plot the diversity maps of structural evolution. 展开更多
关键词 microstructural evolution ENERGETICS KINETICS dynamic system
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DECENTRALIZED CONTROL FOR NONLINEAR DYNAMICAL SYSTEMS: AN L_2-GAIN CONTROL APPROACH
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作者 Gong Cheng(Department of Eletronic Engineering, Northwestern PolytechnicalUniversity, Xi’an, 710072, China)S. Thompson(Department of Mechanical and Manufacturing Engineering, The Queen’s Universityof Belfast, Belfast BT9 5Ah, United Kingdom)Dai Guanzhong( 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 1997年第2期135-143,共9页
A control method is presented for the problem of decentralized stabilizationof large scale nonlinear systems by designing robust controllers, in the sense of L2-gaincontrol, for each subsystem. An uncertainty toleranc... A control method is presented for the problem of decentralized stabilizationof large scale nonlinear systems by designing robust controllers, in the sense of L2-gaincontrol, for each subsystem. An uncertainty tolerance matrix is defined to characterize thedesired robustness leve1 of the overall system. It is then identified that, for a given uncer-tainty tolerance matrix, the design problem is related to the existence of a smooth Positivedefinite solution to a modified Ham ilton -Jacobi - Bellman (H-J-B ) equa tion. The solution,if exists, is exactly the payoff function in terms of the game theory. A decentralized statefeedback law is duly designed, which, under the weak assumption of the zero-state ob-servability on the system, renders the overall closed-loop system aspoptotically stable withan explicitly expressed stability region. Finally, relation between the payoff function andthe uncertainty tolerance matrix is provided, highlighting the 'knowing less and payingmore' philosophy. 展开更多
关键词 nonlinear systems dynamical systems CONTROL Hamilton-Jacobi-Bellman equation
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Gedanken Experiment for Looking at δgtt for Initial Expansion of the Universe and Influence on HUP via Dynamical Systems, with Positive Pre-Planckian Acceleration 被引量:1
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作者 Andrew Walcott Beckwith 《Journal of High Energy Physics, Gravitation and Cosmology》 2016年第4期531-545,共15页
We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration do... We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values). 展开更多
关键词 HUP dynamical systems
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Tangent response in coupled dynamical systems
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作者 闫华 魏平 肖先赐 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第9期217-225,共9页
We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order deriv... We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space. 展开更多
关键词 tangent response generalised synchronisation coupled dynamical systems
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AN EXTENSION OF LEVI-CIVITA’S THEOREM TO NONHOLONOMIC DYNAMICAL SYSTEMS
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作者 Naseer Ahmed 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1990年第2期169-179,共11页
This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient c... This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient condi- tions allowing such extension are obtained and,as an application of the theory a generalization of Routh's motion is presented. 展开更多
关键词 nonholonomic dynamical systems Levi-Civita's theorem Poincaré formalism
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