Computing large deviation prefactors of stochastic dynamical systems based on machine learning

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.

Dynamic Constraint-Driven Event-Triggered Control of Strict-Feedback Systems Without Max/Min Values on Irregular Constraints

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.

THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

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.

Generalized Hopf Bifurcation for Non-smooth Planar Dynamical Systems:the Corner Case

Piece-wise smooth systems are an important class of ordinary differential equations whosedynamics are known to exhibit complex bifurcation scenarios and chaos. Broadly speaking,piece-wise smooth systems can undergo all the bifurcation that smooth ones can. Moreinterestingly, there is a whole class of bifurcation that are unique to piece-wise smoothsystems, such as the bifurcation caused by the geometric shape of the region in which the

Foundations and Applications of Information Systems Dynamics

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.

Distributed dynamic event-based finite-time dissipative synchronization control for semi-Markov switched fuzzy cyber-physical systems against random packet losses

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.

Einstein-Podolsky-Rosen Steering and Nonlocality in Open Quantum Systems

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.

Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques

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.

CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS

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.

Use of Dynamical Systems Modeling to Hybrid Cloud Database

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.

GLOBAL VIEW OF MICROSTRUCTURAL EVOLUTION:ENERGETICS,KINETICS AND DYNAMICAL SYSTEMS

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.

DECENTRALIZED CONTROL FOR NONLINEAR DYNAMICAL SYSTEMS: AN L_2-GAIN CONTROL APPROACH

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.

Gedanken Experiment for Looking at δgtt for Initial Expansion of the Universe and Influence on HUP via Dynamical Systems, with Positive Pre-Planckian Acceleration

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).

Tangent response in coupled dynamical systems

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.

AN EXTENSION OF LEVI-CIVITA’S THEOREM TO NONHOLONOMIC DYNAMICAL SYSTEMS

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.

Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems

Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.

SOME PROBLEMS ON FRACTAL GEOMETRY AND TOPOLOGICAL DYNAMICAL SYSTEMS

This paper is a continuation of [14], some new problems on fractal geometry and topological dynamical systems have been posed.

THE OPTIMAL TRUNCATED LOW-DIMENSIONAL DYNAMICAL SYSTEMS BASED ON FLOW DATABASES

A new theory on the construction of optimal truncated Low-Dimensional Dynamical Systems (LDDSs) with different physical meanings has been developed, The physical properties of the optimal bases are reflected in the user-defined optimal conditions, Through the analysis of linear and nonlinear examples, it is shown that the LDDSs constructed by using the Proper Orthogonal Decomposition (POD) method are not the optimum. After comparing the errors of LDDSs based on the new theory POD and Fourier methods, it is concluded that the LDDSs based on the new theory are optimally truncated and catch the desired physical properties of the systems.

Unified symmetry of Vacco dynamical systems

Based on the total time derivative along the trajectory of the time, we study the unified symmetry of Vacco dynamical systems. The definition and the criterion of the unified symmetry for the system are given. Three kinds of conserved quantities, i.e. the Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity, are deduced from the unified symmetry. An example is presented to illustrate the results.