时标上带强迫项高阶中立型动力方程的振动性与非振动解的存在性

给出时标上一类带强迫项高阶中立型动力方程一切解振动和非振动解存在的若干充分条件.所得结果推广了一些已有的结论.     

时标上δ±移位概周期解的存在唯一性定理(英文)

本文运用时标上微积分理论,δ_±移位概周期函数的性质,及压缩映射原理,研究了时标上非线性和线性动力学方程的δ_±移位概周期解的存在唯一性,分别给出了方程在有限区间和无穷区间上解的具体表达式.最后,将上述研究结果应用于一类具有小参数扰动动力学方程δ_±移位概周期解的存在性研究.     

测度链上一类三阶半线性中立型时滞动力方程的振动准则

利用广义Riccati代换及时标上一些分析技巧给出时标上一类三阶半线性动力方程的振动准则,并利用例子说明其结果的可用性,推广了一些已知的二阶或三阶动力方程振动性的结果.     

时标上一类具阻尼项的二阶动态方程的振荡性

研究了时标上的一类具有阻尼项的二阶非线性中立型变时滞动态方程的振荡性,利用时标上的理论和广义的Riccati变换及不等式技巧,建立了该方程的几个新的振荡准则,这些准则不仅推广和改进了一些已知的结果,而且在时标上统一了具有阻尼项的二阶非线性时滞微分方程和差分方程的振荡性质.并给出了具体实例来说明文章的主要结论.     

时标上一类三阶非线性中立型动力方程的振动性与渐近性

考虑了时标上一类三阶非线性中立型动力方程,得到了该方程一切解振动或渐近趋于零的充分条件.特别地,所得结果推广了一些已有的结论.     

时标上的二阶变时滞动力方程的振动准则

利用广义Riccati技巧及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力方程的振动性,得到了一些新的振动准则.     

三阶非线性中立型变时滞动力方程的渐近性与振动性(英文)

考虑了时标上三阶非线性中立型变时滞动力方程的渐近性和振动性.利用广义Ric-cati技巧与完全平方技巧,获得了方程所有解渐近和振动的准则.所得结果推广了已有三阶动力方程的结果,给出了一些例子加以说明本文的主要结论.     

时标上的三阶非线性中立型变时滞动力方程的振动性与渐进性

考虑了时标上一类三阶非线性中立型变时滞动力方程的振动性和渐进性.利用Riccati变换技巧得到了方程所有解振动或渐进趋于零的充分条件.特别地,所得新结果发展了一些已有结论.并给出了例子加以说明本文的主要结果.     

时标上三阶动力方程边值问题正解的存在性

主要研究时标上三阶动力学方程u~(△△△)(t)=f(t,u(t),u~(△△)(t))在三点边值条件下正解的存在性.主要方法应用格林函数和锥上凹凸函数的性质给出其正解存在的充分条件.     

时标上m点边值问题的广义拟线性方法

利用广义拟线性方法研究了时标上非线性动力方程m点边值问题,给出了一种有效求解方法.     

Dynamic Complexities of a Three-Species Beddington-DeAngelis System with Impulsive Control Strategy

By introducing the impulsive control strategy, the dynamical properties of the three-species food chain systems with Beddington-DeAngelis functional response are investigated. Using the Floquet theory of impulsive differential equations and small amplitude perturbation techniques, we prove that there exists an asymptotically locally stable prey-free periodic solution under some conditions, and permanence conditions are established via the comparison theorem. Furthermore, from numerical examples, we figure out that the system has complex dynamic behaviors.     

Analysis of and numerical schemes for a mouse population model in Hantavirus epidemics

This paper considers a non-linear system of ordinary differential equations, which arises in the study of hantavirus epidemics. The system has the property that the total population obeys the logistic equation. For this system, we use linearization and the dynamical properties of the logistic equation to analyze the dynamics of the subpopulation system. In view of the usual numerical instabilities associated with standard finite difference methods used for simulating such systems, we construct non-standard finite difference (NSFD) schemes, which preserve the dynamic properties of the system, and may therefore be used for its simulation.     

A generalization of Vinograd's theorem for dynamical systems

The theory of dynamical systems has been expanded by the introduction of local dynamical systems [10, 4, 9] and local semidynamical systems [1]. Using integral curves of autonomous ordinary differential equations to illustrate these generalizations, we find that, roughly, the integral curves form a local dynamical system if solutions exist and are unique without requiring existence for all time, and the integral curves form a local semidynamical system if solutions exist and are unique in the positive sense but need not exist for all positive time. In addition to autonomous ordinary differential equations, the enlarged theory of dynamical systems has applications to nonautonomous ordinary differential equations, certain partial differential equations, functional differential equations, and Volterra Integral equations [9, 1, 2, 8], respectively. All of these have metric phase spaces. Since many dynamic considerations are invariant to reparameterizations, it is of interest to known when a local dynamical (or semidynamical) system can be reparameterized to yield a “global” dynamical (or semidynamical) system. For autonomous ordinary differential equations, Vinograd [7] has shown that the local dynamical system on an open subset ofRⁿ formed by integral curves is isomorphic (in the sense of Nemytskii and Stepanov) to a global dynamical system. In an extensive study of isomorphisms, Ura [12] has expanded the Gottschalk-Hedlund notion of an isomorphism and restated Vinograd's result in terms of a reparameterization. In this paper we study the problem of finding a global dynamical (or semidynamical) system which is isomorphic to a given local system. A necessary and sufficient condition is found which is then used to show that the Vinograd result holds on metric spaces.     

Navier-Stokes方程五模类Lorenz方程组的动力学行为及数值仿真

本文对平面正方形区域上不可压缩的Navier-Stokes方程,进行傅立叶展开后,截断得到五模类Lorenz方程组.给出了该方程组定常解及其稳定性的讨论,证明了该方程组吸引子的存在性,并对其全局稳定性进行了分析和讨论,数值模拟了雷诺数在一定范围内变化时,类Lorenz方程组的动力学行为.     

Tracking a reference solution of a control system of phase field equations

We consider the problem of tracking a reference solution of a dynamical system described by a pair of distributed differential equations, the phase field equations. To solve this problem, we propose an algorithm based on Yu.S. Osipov’s theory of dynamic inversion and on N.N. Krasovskii’s extremal shift method developed in the theory of positional differential games.     

Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions

This paper deals with the stability analysis of a class of uncertain switched systems on non-uniform time domains. The considered class consists of dynamical systems which commute between an uncertain continuous-time subsystem and an uncertain discrete-time subsystem during a certain period of time. The theory of dynamic equations on time scale is used to study the stability of these systems on non-uniform time domains formed by a union of disjoint intervals with variable length and variable gap. Using the concept of common Lyapunov function, sufficient conditions are derived to guarantee the asymptotic stability of this class of systems on time scale with bounded graininess function. The proposed scheme is used to study the leader–follower consensus problem under intermittent information transmissions.     

A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton–Jacobi equations

We investigate the large-time behavior of the value functions of the optimal control problems on the n-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of view of the study on partial differential equations, it is equivalent to consider viscosity solutions of quasi-monotone weakly coupled systems of Hamilton–Jacobi equations. The large-time behavior of viscosity solutions of this problem has been recently studied by the authors and Camilli, Ley, Loreti, and Nguyen for some special cases, independently, but the general cases remain widely open. We establish a convergence result to asymptotic solutions as time goes to infinity under rather general assumptions by using dynamical properties of value functions.     

On structural transformations of equations of perturbed motion for a certain class of dynamical systems

We consider a general method for structural transformations of one class of dynamical systems with gyroscopic forces, which enables us to remove gyroscopic terms from the original equations of perturbed motion. Without changing the qualitative properties of these equations, this method simplifies their investigation.     

Long-Time Stabilization of Solutions to the Ginzburg–Landau Equations of Superconductivity

 The long-time dynamical properties of solutions (φ,A) to the time-dependent Ginzburg–Landau (TDGL) equations of superconductivity are investigated. The applied magnetic field varies with time, but it is assumed to approach a long-time asymptotic limit. Sufficient conditions (in terms of the time rate of change of the applied magnetic field) are given which guarantee that the dynamical process defined by the TDGL equations is asymptotically autonomous, i.e., it approaches a dynamical system as time goes to infinity. Analyticity of an energy functional is used to show that every solution of the TDGL equations asymptotically approaches a (single) stationary solution of the (time-independent) Ginzburg–Landau equations. The standard “φ = − ∇ · A” gauge is chosen. (Received 30 June 2000; in revised form 30 December 2000)     

Long-Time Stabilization of Solutions to the Ginzburg–Landau Equations of Superconductivity

 The long-time dynamical properties of solutions (φ,A) to the time-dependent Ginzburg–Landau (TDGL) equations of superconductivity are investigated. The applied magnetic field varies with time, but it is assumed to approach a long-time asymptotic limit. Sufficient conditions (in terms of the time rate of change of the applied magnetic field) are given which guarantee that the dynamical process defined by the TDGL equations is asymptotically autonomous, i.e., it approaches a dynamical system as time goes to infinity. Analyticity of an energy functional is used to show that every solution of the TDGL equations asymptotically approaches a (single) stationary solution of the (time-independent) Ginzburg–Landau equations. The standard “φ = − ∇ · A” gauge is chosen.