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Some Dynamical Properties in Set-valued Discrete Systems 被引量:2
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作者 马先峰 廖公夫 李勇 《Northeastern Mathematical Journal》 CSCD 2005年第1期5-8,共4页
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved.... 1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X). 展开更多
关键词 set-valued discrete system MINIMALITY topologically weak mixing topo-logical mixing
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A Family of Integrable Rational Semi-Discrete Systems and Its Reduction
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作者 徐西祥 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第2期205-210,共6页
Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are co... Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out. 展开更多
关键词 semi-discrete system discrete zero curvature equation Lax pair Hamiltonian form Liouville integrability
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DIFFERENCE DISCRETE SYSTEM OF EULER-BEAM WITH ARBITRARY SUPPORTS AND SIGN-OSCILLATORY PROPERTY OF STIFFNESS MATRICES
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作者 王其申 王大钧 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第3期393-398,共6页
The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory... The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory of oscillatory matrix, the signoscillatory property of stiffness matrices of this system was proved, and the necessary and sufficient condition for the system to be positive was obtained completely. 展开更多
关键词 Euler-beam difference discrete systems stiffness matrices sign-oscillatory property
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Generalized synchronization of discrete systems
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作者 马忠军 刘曾荣 张刚 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第5期609-614,共6页
Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive a... Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples. 展开更多
关键词 generalized synchronization COUPLING discrete systems
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Distance-Stability of Nonlinear Discrete Systems
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作者 曹守明 肖会敏 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第3期45-49,共5页
In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov fu... In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided. 展开更多
关键词 NONLINEAR discrete systems distance-stability Gauss-Seidel iteration method
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Constructing exact solutions to discrete systems with the trial function method
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作者 Taogetusang Sirendaoerji 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第3期286-294,共9页
Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic ... Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear (2 + 1) dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems. 展开更多
关键词 the trial function method discrete system (2+1)-dimensional Hybrid-lattice system exact solitary wave solution
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LINEAR ACTIVE STRUCTURES AND MODES (Ⅱ) —DISCRETE SYSTEMS AND BEAMS
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作者 王永刚 龚靖School of Civil Engineering and Mechanics +10 位作者 Xi'an Jiaotong University Xi'an 710049 P.R.China Department of Civil Engineering Northeast China Institute of Electric Power Jilin 132012 P.R.China 张景绘School of Civil Engineering and Mechanics Xi'an Jiaotong University Xi'an 710049 P.R.China 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第8期854-862,共9页
The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active be... The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures. 展开更多
关键词 I) ". The characteristics of the active discrete systems and active beams were discussed especially the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-s
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A Modified Stability Analysis of Two-Dimensional Linear Time Invariant Discrete Systems within the Unity-Shifted Unit Circle
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作者 Periyasamy Ramesh 《Circuits and Systems》 2016年第3期110-118,共9页
This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e... This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme. 展开更多
关键词 TWO-DIMENSIONAL Characteristics Equation Unity Shifting Inner Determinant Linear Time Invariant discrete systems Stability
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Certain Algebraic Test for Analyzing Aperiodic Stability of Two-Dimensional Linear Discrete Systems
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作者 P. Ramesh 《Circuits and Systems》 2016年第6期718-725,共8页
This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equiv... This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique. 展开更多
关键词 Routh Table Aperiodic Stability Characteristics Equation TWO-DIMENSIONAL Linear discrete systems
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Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control 被引量:2
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作者 Adel Ouannas Amina Aicha Khennaoui +2 位作者 Shaher Momani Viet-Thanh Pham Reyad El-Khazali 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第5期174-181,共8页
This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system wi... This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium.Through phase portrait,bifurcation diagrams,and largest Lyapunov exponents,it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors.Also,different tests are used to confirm the existence of chaos,such as 0-1 test and C0 complexity.In addition,the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique.Furthermore,based on the fractional linearization method,a one-dimensional controller to stabilize the new system is proposed.Numerical results are presented to validate the findings of the paper. 展开更多
关键词 discrete chaos discrete fractional calculus hidden attractor
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H_∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay 被引量:1
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作者 Bai-Da Qu Control Science and Engineering Center, Southern Yangtze University, 1800 Lihu Road, Wuxi 214122, PRC 《International Journal of Automation and computing》 EI 2005年第2期107-113,共7页
In this paper, H ∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a ... In this paper, H ∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H ∞ performance indices is induced, and then a strategy for H ∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H ∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach. Keywords Multi-time-delay - discrete time system - LMI - delay-dependent - H ∞ control Bai-Da Qu received B. S. degree in electrical automation from Fuxin Mining Institute, China in 1982, M. Eng. degree from Hefei University of Polytechnology in 1990, and Ph.D from Northerneastern University in 1999. He was an electro-mechanical engineer at Erdaohezi Mine, Heilongjiang, China from 1982 to 1990, a Lecturer, Senior Engineer, Associate Professor and Professor in Shenyang Institue of Technology from 1990 to 2002. He is currently a professor in Communication and Control Engineering School, Southern Yangtze University. His research interests include control theory and applications (robust control, H ∞ control, time-delay systems, complex systems), system engineering (modeling, analysis and simulation, MIS,CMIS), power-electronics and electrical driving, signal detecting and process, industrial automation. 展开更多
关键词 Multi-time-delay discrete time system LMI DELAY-DEPENDENT H control
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Lyapunov Inequalities of Nonlinear Discrete Systems
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作者 ZHOU Mei-xiu WANG Xin-zhen 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第2期182-190,共9页
In this paper, we study the nonlinear discrete systems and obtain several lyapunov inequalities for them. Then we give the application for lyapunov inequality.
关键词 Lyapunov inequality nonlinear discrete equation generalized zero
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A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model
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作者 Manish Tiwari Amit Dhawan 《Circuits and Systems》 2012年第1期17-22,共6页
A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular mo... A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular model, called Forna- sini-Marchesini (FM) second model was proposed by Fornasini and Marchesini in 1978. The aim of this paper is to present a survey of the existing literature on the stability of FM second model. 展开更多
关键词 2-D discrete systems FM SECOND MODEL ASYMPTOTIC Stability LYAPUNOV Methods
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Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model
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作者 Manish Tiwari Amit Dhawan 《Journal of Signal and Information Processing》 2012年第2期252-258,共7页
This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New line... This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function. 展开更多
关键词 Guaranteed Cost Control Linear Matrix INEQUALITY LYAPUNOV Methods ROBUST Stability 2-D discrete systemS UNCERTAIN systemS
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Dissipative Discrete System with Nearest-Neighbor Interaction for the Nonlinear Electrical Lattice
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作者 Saidou Abdoulkary Tibi Beda +3 位作者 Serge Y.Doka Fabien II Ndzana Louis Kavitha Alidou Mohamadou 《Journal of Modern Physics》 2012年第6期438-446,共9页
A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This ... A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability. 展开更多
关键词 Generalized Dissipative discrete Complex Ginzburg-Landau Equation discrete Lange Newell-Criterion Pulse Trains Solitary Patterns
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Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems
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作者 Yunfeng Hu Chong Zhang +4 位作者 Bo Wang Jing Zhao Xun Gong Jinwu Gao Hong Chen 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第2期344-361,共18页
Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning ... Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process. 展开更多
关键词 Adaptive control control system synthesis data-driven iterative learning control neurocontroller nonlinear discrete time systems
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A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY
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作者 冯立超 张春艳 +1 位作者 曹进德 武志辉 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1145-1164,共20页
Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existi... Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form. 展开更多
关键词 hybrid neutral stochastic differential delay system discrete feedback control general stabilization polynomial stabilization
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Discrete Choice Models and Artificial Intelligence Techniques for Predicting the Determinants of Transport Mode Choice--A Systematic Review
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作者 Mujahid Ali 《Computers, Materials & Continua》 SCIE EI 2024年第11期2161-2194,共34页
Forecasting travel demand requires a grasp of individual decision-making behavior.However,transport mode choice(TMC)is determined by personal and contextual factors that vary from person to person.Numerous characteris... Forecasting travel demand requires a grasp of individual decision-making behavior.However,transport mode choice(TMC)is determined by personal and contextual factors that vary from person to person.Numerous characteristics have a substantial impact on travel behavior(TB),which makes it important to take into account while studying transport options.Traditional statistical techniques frequently presume linear correlations,but real-world data rarely follows these presumptions,which may make it harder to grasp the complex interactions.Thorough systematic review was conducted to examine how machine learning(ML)approaches might successfully capture nonlinear correlations that conventional methods may ignore to overcome such challenges.An in-depth analysis of discrete choice models(DCM)and several ML algorithms,datasets,model validation strategies,and tuning techniques employed in previous research is carried out in the present study.Besides,the current review also summarizes DCM and ML models to predict TMC and recognize the determinants of TB in an urban area for different transport modes.The two primary goals of our study are to establish the present conceptual frameworks for the factors influencing the TMC for daily activities and to pinpoint methodological issues and limitations in previous research.With a total of 39 studies,our findings shed important light on the significance of considering factors that influence the TMC.The adjusted kernel algorithms and hyperparameter-optimized ML algorithms outperform the typical ML algorithms.RF(random forest),SVM(support vector machine),ANN(artificial neural network),and interpretable ML algorithms are the most widely used ML algorithms for the prediction of TMC where RF achieved an R2 of 0.95 and SVM achieved an accuracy of 93.18%;however,the adjusted kernel enhanced the accuracy of SVM 99.81%which shows that the interpretable algorithms outperformed the typical algorithms.The sensitivity analysis indicates that the most significant parameters influencing TMC are the age,total trip time,and the number of drivers. 展开更多
关键词 Machine learning techniques AI transport mode choice discrete choice model sustainable transportation
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Model Order Reduction Methods for Discrete Systems via Discrete Pulse Orthogonal Functions
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作者 XIE Zhen TANG Shengguo WANG Zhaohong 《新疆大学学报(自然科学版中英文)》 CAS 2024年第6期641-650,共10页
This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear syst... This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods. 展开更多
关键词 model order reduction discrete linear systems discrete bilinear systems discrete pulse orthogonal functions
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Controllability of Nonlinear Discrete Systems with Degeneracy
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作者 Yue LYU Xue-li TAN +1 位作者 Xue YANG Yong LI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2023年第2期293-305,共13页
This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,s... This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results. 展开更多
关键词 nonlinear discrete systems CONTROLLABILITY DEGENERACY Fredholm operators coincidence degree theory
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