若干类时滞切换系统的稳定性问题

主要研究了镇定切换系统的鲁棒稳定性问题.用切换lyapunov函数方法,通过定义指标函数,讨论了基于切换lyapunov函数的若干类时滞切换系统的稳定性问题,用矩阵不等式研究了时滞,时滞摄动和不确定时滞的切换系统的鲁棒稳定性.     

Systems of generalized quasivariational inclusions problems with applications to variational analysis and optimization problems

In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result, we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints. This research was supported by the National Science Council of the Republic of China.     

Ten years of genetic fuzzy systems: current framework and new trends

Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. Neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms.The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems. After a brief introduction to models and applications of genetic fuzzy systems, the field is overviewed, new trends are identified, a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated, and open questions that remain to be addressed in the future are raised. The paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems.     

A theory for synchronization of dynamical systems

In this paper, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical systems. The concepts on synchronization of two or more dynamical systems to specific constraints are presented. The synchronization, desynchronization and penetration of multiple dynamical systems to multiple specified constraints are discussed, and the necessary and sufficient conditions for such synchronicity are developed. The synchronicity of two dynamical systems to a single specific constraint and to multiple specific constraints is investigated. Finally, the synchronization and the corresponding complexity for multiple slave systems with multiple master systems are discussed briefly. The meaning of synchronization for dynamical systems with constraints is extended as a generalized, universal concept. The theory presented in this paper may be as a universal theory for dynamical systems. The paper provides a theoretic frame work in order to control slave systems which can be synchronized with master systems through specific constraints in a general sense.     

Existence theorems of systems of variational inclusion problems with applications

In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results, we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems of variational inclusion constraints, bilevel problem with systems of constraints.     

Asymptotic behavior of solutions of pulse systems with small parameter and markov switchings. I. Uniform boundedness of solutions

We consider pulse systems with Markov switchings. We study the problems of uniform boundedness of solutions of these systems and the stability of the systems with respect to the limit equation.     

Generalization of the Jurdjevic-Quinn theorem and stabilization of bilinear control systems with periodic coefficients: II

We prove sufficient conditions for the uniform global asymptotic stabilization of the origin for bilinear time-varying systems that can be reduced by a Lyapunov transformation to bilinear periodic systems with time-invariant drift, in particular, for bilinear periodic systems with time-varying drift. We obtain corollaries for consistent systems.     

Existence of periodic solutions of sublinear Hamiltonian systems

The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need additional conditions to ensure the existence of periodic bouncing solutions.     

On the noncoincidence of two sets of linear systems

We show that the set of linear systems reducible by a generalized Lyapunov transformation to diagonal systems with ordered diagonal does not coincide with the set of linear systems whose Lyapunov exponents are invariant under exponentially decaying perturbations.     

Asymptotic behavior of solutions of pulse systems with small parameter and markov switchings. II. Weak convergence of solutions

We consider pulse systems with Markov switchings. We study the problem of the uniform boundedness of solutions of such systems and the stability of the systems with respect to the limit equation.     

Sensitivity of solutions to systems of optimality conditions under the violation of constraint qualifications

A survey is given of old and new results on the sensitivity of solutions to systems of optimality conditions with respect to parametric perturbations. Results of this kind play a key role in subtle convergence analysis of various constrained optimization algorithms. General systems of optimality conditions for problems with abstract constraints, Karush-Kuhn-Tucker systems for mathematical programs, and Lagrange systems for problems with equality constraints are examined. Special attention is given to the cases where the traditional constraint qualifications are violated.     

Dynamical behavior of Lotka–Volterra competition systems: non-autonomous bistable case and the effect of telegraph noise

This article is concerned with the study of trajectory behavior of Lotka–Volterra competition bistable systems and systems with telegraph noises. We proved that for bistable systems, there exists a unique solution, bounded above and below by positive constants. The oscillatory situation of systems with telegraph noises is pointed out.     

Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations

In this paper, we provide a method to solve the Cauchy problem of systems of quasi‐linear parabolic equations, such systems can be transformed to the systems of linear parabolic equations with variable coefficients via the hodograph transformations. Our approach to solve the linear systems with variable coefficients is to use their fundamental solutions, which are constructed by using the Lie's symmetry method. In consequence, we can derive explicit solutions to the Cauchy problem of the quasi‐linear systems in terms of the solutions of the linear systems and the hodograph transformations relating to the quasi‐linear and the linear systems.     

Complete group classification of systems of two linear second-order ordinary differential equations

We give a complete group classification of the general case of linear systems of two second-order ordinary differential equations excluding the case of systems which are studied in the literature. This paper gives the initial step in the study of nonlinear systems of two second-order ordinary differential equations. It can also be extended to systems of equations with more than two equations. Furthermore the complete group classification of a system of two linear second-order ordinary differential equations is done. Four cases of linear systems of equations with inconstant coefficients are obtained.     

Preservation of reliability classes under the formation of coherent systems

The preservation of reliability aging classes under the formation of coherent systems is a relevant topic in reliability theory. Thus, it is well known that the new better than used class is preserved under the formation of coherent systems with independent components. However, surprisingly, the increasing failure rate class is not preserved in the independent and identically distributed case, that is, the components may have the (negative) aging increasing failure rate property, but the system does not have this property. In this paper, we study conditions for the preservation of the main reliability classes under the formation of general coherent systems. These results can be applied both for systems with independent or dependent components. We consider both the case of systems with identically distributed components and the case of systems with components having different distributions. Copyright © 2013 John Wiley & Sons, Ltd.     

On the structure of additive systems of integers

A sum-and-distance system is a collection of finite sets of integers such that the sums and differences formed by taking one element from each set generate a prescribed arithmetic progression. Such systems, with two component sets, arise naturally in the study of matrices with symmetry properties and consecutive integer entries. Sum systems are an analogous concept where only sums of elements are considered. We establish a bijection between sum systems and sum-and-distance systems of corresponding size, and show that sum systems are equivalent to principal reversible cuboids, which are tensors with integer entries and a symmetry of ‘reversible square’ type. We prove a structure theorem for principal reversible cuboids, which gives rise to an explicit construction formula for all sum systems in terms of joint ordered factorisations of their component set cardinalities.

     

Stability and positivity of equilibria for subhomogeneous cooperative systems

Building on recent work on homogeneous cooperative systems, we extend results concerning stability of such systems to subhomogeneous systems. We also consider subhomogeneous cooperative systems with constant input, and relate the global asymptotic stability of the unforced system to the existence and stability of positive equilibria for the system with input.     

Hyperbolic systems of conservation laws with a symmetry

Hyperbolic systems of conservaiton laws with a symmetry are studied. Some peculiar phenomena for such systems are shown. Admissibility criteria for solutions to such systems are discussed. propagation and cancellation of initial oscillations for the systems are classified. As a byproduct of this study, an existence theorem of global solutions for the Cauchy of the systems is established.     

偏微分方程的吸引子

Abstract. In this paper the reaction-diffusion systems and the damped wave systems with non-linear terms of gradient form are studied ,and the conditions for making them to be gradient sys-tems are given. So the structure of attractors is clear and simple in some sense by the known re-sult. Some examples are given. Also the reaction-diffusion systems with general nonlinear termsare discussed.     

Damped vibrations of the beam systems in rotational transportation

The major aim of this thesis is dynamical analysis of systems in rotational transportation with taking into consideration in the mathematical models the damping forces. The dissipation of energy in form of damping is inseparable connected with motion of analyzed systems. Up to now modelling of rod and beam systems in transportation was very often based on simplification and reduction of damping effect and on the other side the considerations very rarely apply to systems where the transportation effect was took into consideration. In this thesis the dynamical flexibility of the damped beam systems in transportation was presented. Analyzing systems were assumed as simple homogenous beam systems with symmetrical cross-section constant on whole length of the system. Most popular technical applications of such systems are put into use in propellers and sails of wind power plant, main, auxiliary rotors of helicopters, turbines, etc. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)