INTEGRABILITY AND LINEARIZABILITY FOR A CLASS OF CUBIC KOLMOGOROV SYSTEMS

The integrability and linearizability for a class of cubic Kolmogorov systems are studied. A recursive formula to compute the saddle quantities of the systems is deduced firstly, and integrable conditions for the systems are obtained. Then a recursive formula to compute the coefficients of the normal form for saddle points of the systems is also applied. Finally linearizable conditions of the origin for the systems are given. Both formulas to find necessary conditions are all linear and readily done using c...     

时不变和时变的Caputo分数阶时滞微分系统的常数变易公式

This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall＇s integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations.     

NONDEGENERACY OF POSITIVE SOLUTIONS TO HOMOGENEOUS SECOND-ORDER DIFFERENTIAL SYSTEMS AND ITS APPLICATIONS

This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.     

RECURSIVENESS OF ZERO STRUCTURES FOR SYSTEM MATRICES OF INTERCONNECTED LINEAR SYSTEMS VIA MODULE THEORETIC TOOLS

The importance of the zeros of multwariable linear systems is well-knoiun in terms of measure obstructions to the controllability and the. observability. In this paper, a recursive decarnposi Am oj interconnected systems is outlined by taking into account the sequential structure of the connnections. The paper extends the, coordinate, module-theoretic studies from the elementary algebraic systems theory to include the case oj such linear interconnected systems which need not to be controllable or observable. Also, the properties of controllability and observability, the decoupling zeros and the signal Making issues are characterized.     

A KAM-type Theorem for Generalized Hamiltonian Systems

In this paper we mainly concern the persistence of invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensional tori might be elliptic, hyperbolic, or of mixed type.     

The Partial Stability for Linear Discrete Systems

In this paper, we study the partial stability of linear discrete systems by means of Liapunov's functions of quadratic form. We obtain a necessary and sufficient condition for the system being stable with respect to part of variables and generalize Liapunov's equation to the partial stability of linear discrete systems. A method of constructing Liapunov's function of quadratic form for the stability of the systems is given.     

ESTIMATES OF N-FUNCTION AND m-FUNCTION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS

We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.     

CONTROLLABILITY AND OBSERVABILITY FOR A CLASS OF FRACTIONAL-ORDER IMPULSIVE SYSTEMS

This paper studies the controllability and observability for a class of fractionalorder impulsive systems.First,the basic acknowledgement of fractional-order systems is presented.Then the solution of the fractional-order impulsive systems is given.Finally,necessary and sufficient criteria for controllability and observability are obtained.     

Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators北大核心CSCD

Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

CHINESE ANNALS OF MATHEMATICS Vol.4 Ser.A No.1 CONTENTS AND ABSTRACTS The Third Boundary Value Problem for Elliptic Systems of Second Order

In this paper,we discuss the third boundary elliptic systems of second order(1.1)in a multiplyconnceted domain.We first prove that problem III of the harmonic function has a unique solutionand estabilish the integral expression of solutions for problem III of the systems(1.1).Next,usingthe above results,a priori estimates for solutions of problem Ill of the systems(1.1)and Leray-Schauder theorem,we obtain the result on the solvability of problem III for the nonlitnear systems(1.1)satisfying some conditions.     

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.     

复杂系统的一般数学框架(Ⅰ)

复杂系统的基本和最简单的结构就是网络.根据这一思想,本系列论文拟发展一套处理复杂系统的新数学框架.本文详细论述了系统的概念、一般描述方法:系统=(硬部,软部,环境)和局整关系,包括子系统、元素与系统的关系和系统与系统的关系;给出了系统运算的基本法则;简要论述了系统的软、硬部之间的诱导转化.     

线性连续衰退记忆系统的可分性

为逼近建模和辨识问题的需要,讨论线性时变连续有界输入有界输出稳定衰退记忆系统的不同子类．从衰退记忆系统的子类包括概周期系统,渐近周期系统,渐近强周期系统,找到了LTV系统的可分子空间即渐近强周期系统．     

A model of general systems

In this paper a mathematical model of general systems with not only one, but also more than one relation between the objects of the systems, was introduced. Among others, the concepts of partial systems, similarity of systems, embeddability of systems and free sum of systems were introduced. The following theorem was proved: there is no system whose object set consists of all systems.     

非线性退化时滞微分控制系统的函数能控性

本文讨论非线性退化时滞微分控制系统．首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据．     

自治Birkhoff系统的广义正则变换和辛算法研究

研究了自治Birkhoff系统的广义正则变换,将Hamilton系统的辛算法推广到Birkhoff系统,通过引入凯莱变换和生成函数法构造Birkhoff方程的Birkhoff的辛差分格式,同时讨论了Birkhoff差分格式的辛算法.     

Poincaré and Poincaré-Cartan integral invariants of a generalized Hamiltonian system

IntroductionUsually, only conservative or self-adjoint systems admit Hamiltonian canonical structure,i. e., a symplectic form and a Hamiltonian for such systems, under the experimenters' coordinateand time variables. Thus Hamilton's canonicaJ eqllations do not admit direct universality. ASa generajization of Hamilton's equations, Birkhoff's equations that are self-adjoint realize thedirect universajity and preserve the symbiotic character among the canonical formulation ofvariational princi…     

Sensitivity of non-autonomous discrete dynamical systems

In this paper, the sensitivity for non-autonomous discrete systems is investigated. First of all, two sufficient conditions of sensitivity for general non-autonomous dynamical systems are presented. At the same time, one stronger form of sensitivity, that is, cofinite sensitivity, is introduced for non-autonomous systems. Two sufficient conditions of cofinite sensitivity for general non-autonomous dynamical systems are presented. We generalized the result of sensitivity and strong sensitivity for autonomous discrete systems to general non-autonomous discrete systems, and the conditions in this paper are weaker than the correlated conditions of autonomous discrete systems.     

Controller design for stabilizing bilinear systems with state-based switching

Some nonlinear systems can be approximated by switching bilinear systems. In this paper, we proposed a method to design state-based stabilizing controller for switching bilinear systems. Based on the similarity between switching bilinear systems and switching linear systems, corresponding switching linear systems are obtained for switching bilinear systems by applying state-based feedback control laws. Instead, we consider asymptotically stabilizing the corresponding switching linear system through solving a number of relaxed LMI conditions. Stabilizing controllers for switching bilinear systems can be derived based on the results of the corresponding switching linear systems. The stability of the controller is proved step by step through the decreasing of the multiple Lyapunov functions along the state trajectory. The effectiveness of the method is demonstrated by both a theoretical example and an example of urban traffic network with traffic signals.     

相对论性Birkhoff系统动力学方程的代数结构与Poisson积分方法

定义相对论性Ｐｆａｆｆ作用量,得到相对论性Ｐｆａｆｆ Ｂｉｒｋｈｏｆｆ原理和相对论性Ｂｉｒｋｈｏｆｆ方程．证明了自治形式和半自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程具有相容代数结构和Ｌｉｅ代数结构;一般非 自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程没有代数结构．研究一种特殊的非自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程,它具有相容代数结构和Ｌｉｅ容许代数结构．给出相对论性Ｂｉｒｋｈｏｆｆ方程的Ｐｏｉｓｓｏｎ积分 方法．最后给出应用性实例．