On almost reducible systems with almost periodic coefficients

Let x=A(t)x be a system of two linear ordinary differential equations with almost periodic coefficients. Then there exists for any positive ε an almost reducible system of equations x=B(t)x with almost periodic coefficients and such that sup ∥A(t)?B (t)∥<ε.-∞相似文献   

On almost periodic solutions of logistic delay differential equations with almost periodic time dependence

In this paper, we study almost periodic logistic delay differential equations. The existence and module of almost periodic solutions are investigated. In particular, we extend some results of Seifert in [G. Seifert, Almost periodic solutions of certain differential equations with piecewise constant delays and almost periodic time dependence, J. Differential Equations 164 (2000) 451–458].     

Periodic and almost periodic solutions of strongly non-linear impulsive systems

The problem of the existence and stability of periodic and almost periodic solutions of strongly non-linear impulsive systems is investigated. The Poincaré method [1] is justified for the case of an isolated generating solution. A dynamical system consisting of a bead on a vibrating surface is considered as an example.

The small parameter method for investigating systems with discontinuous solutions was previously applied [2, 3] to the case when the periodic solution is non-isolated.

A method is used below for reducing the investigation of a system of equations with impulsive actions on surfaces to equations with fixed moments of inpulsive action.     

Weak almost periodic motions,minimality and stability in impulsive semidynamical systems

In this paper, we study topological properties of semidynamical systems whose continuous dynamics are interrupted by abrupt changes of state. First, we establish results which relate various concepts as stability of Lyapunov, weakly almost periodic motions, recurrence and minimality. In the sequel, we study the stability of Zhukovskij for impulsive systems and we obtain some results about uniform attractors.     

On the stability in periodic and almost periodic difference systems

In this paper we consider the system of difference equations

     

On linear almost periodic pulse systems

For a linear almost periodic system under pulse influence, the conditions are established under which this system is reducible (by a linear change of variables with a discontinuous almost periodic matrix) to a system without pulses but with a Bohr almost periodic right-hand side. The set of linear almost periodic pulse systems possessing only bounded solutions is studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 105–113, January, 1993.     

Global dynamics of the periodic logistic system with periodic impulsive perturbations

This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions.     

Existence of almost periodic solutions for neutral delay difference systems

In this paper, the existence of almost periodic solutions is studied via the Lyapunov function. Razumikhin type theorems are established on the existence, uniqueness and uniformly asymptotic stability of almost periodic solutions. Two examples are given to explain our results.      

Pseudo almost periodic in distribution solutions and optimal solutions to impulsive partial stochastic differential equations with infinite delay

In this paper, we study a general class of impulsive partial stochastic differential equations with infinite delay and pseudo almost periodic coefficients in Hilbert spaces. Firstly, a more appropriate concept of pseudo almost periodic in distribution for stochastic processes of infinite class is introduced. Secondly, the existence of pseudo almost periodic in distribution mild solutions is investigated by utilizing the interpolation theory, the stochastic analysis techniques and fixed point theorem. The existence of optimal mild solutions of the systems is also proved. Finally, an example is provided to show the effectiveness of the theoretical results.     

具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

The positive almost periodic solution for Nicholson-type delay systems with linear harvesting terms

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for a class of Nicholson-type delay system with linear harvesting terms. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.     

Positive periodic solutions of nonautonomous delay competitive systems with weak Allee effect

This paper considers a nonautonomous Lotka–Volterra type multispecies competitive system with weak Allee effect and delays. The model has the intraspecific competition terms defined by sign changing functions which depend on population density monotonically and time periodically. An existence theorem of positive periodic solutions is established using the coincidence degree theory. Furthermore, for the case of constant delays, a sufficient condition for the positive periodic solution to be globally attractive is proved with the Lyapunov method so that the system attains permanence.     

Globally exponential stability of periodic solutions for nonlinear impulsive delay systems

In this paper, the existence and globally exponential stability of periodic solutions for nonlinear impulsive delay systems are studied. Our results improve and generalize some of the previous results found in the literature. Two examples are discussed to illustrate our results.     

Chaos in almost periodic systems

Let be an almost periodic differential equation with a hyperbolic almost periodic solutionu(t) and another hyperbolic solutionv(t) satisfying ¦v(t)–u(t)¦0 as ¦t¦. It is shown that the solutions of such an equation exhibit chaotic behavior.

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Zusammenfassung Sei eine fastperiodische Differentialgleichung mit einer fastperiodischen hyperbolischen Lösungu(t) und seiv(t) eine weitere hyperbolische Lösung für welche ¦v(t)–u(t)¦0 für ¦t¦. Es wird gezeigt, daß die Differentialgleichung unter diesen Bedingungen chaotisches Verhalten aufweist.

     

概周期系统概周期解的存在唯一性

运用Ｌｉａｐｕｎｏｖ函数，研究了概周期系统概周期解的存在唯一性，得到了一个方便应用的判定定理．     

Tracking almost periodic signals under white noise perturbations

A result of the "law of large numbers" type is obtained for the cost of tracking almost periodic signals if the deterministic optimal feedback law is used in the presence of white noise perturbations     

Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for a class of Nicholson-type delay system. Under proper conditions, we establish some criteria to ensure that the solutions of this system converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.