Impulsive control for a class of neural networks with bounded and unbounded delays

In this paper, we study the problem of global exponential stability for a class of impulsive neural networks with bounded and unbounded delays and fixed moments of impulsive effect. We establish stability criteria by employing Lyapunov functions and Razumikhin technique. An illustrative example is given to demonstrate the effectiveness of the obtained results.     

Antiperiodic solutions of fourth‐order impulsive differential equation

In this paper, the existence of antiperiodic solutions for fourth‐order impulsive differential equation is obtained by variational approaches and results on the auxiliary system. It is interesting that there is no growth restraint on nonlinear terms and impulsive terms. Besides, any minimizing sequence is bounded in a closed convex set of a space composed of Lipschitzian functions with the appearance of antiperiodic boundary value conditions.     

BOUNDEDNESS OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

In this paper, we study the boundedness of a class of impulsive functional differential equations with infinite delays. We establish a uniform boundedness theorem and a uniformly ultimate boundedness theorem, which show that a certain impulsive perturbation can make an unbounded system into uniformly bounded, even uniformly ultimate bounded.     

Exponential stability of impulsive stochastic functional differential equations

In this paper, we investigate the pth moment and almost sure exponential stability of impulsive stochastic functional differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Meanwhile, an example and simulations are given to show that impulses play an important role in pth moment and almost sure exponential stability of stochastic functional differential equations with finite delay.     

APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS

In this article, we study the approximate controllability results for an integroquasilinear evolution equation with random impulsive moments under sufficient conditions.The results are obtained by the theory of C_0 semigroup of bounded linear operators on evolution equations and using trajectory reachable sets. Finally, we generalize the results too with and without fixed type impulsive moments.     

具有线性扰动的线性脉冲微分系统的有界增长

本文介绍了脉冲微分系统的有界增长的概念，并进一步讨论了具有线性扰动的线性脉冲微分系统的有界增长问题，得到了反映无扰和扰动两种情形下脉冲微分系统有界增长关系的定理。     

一类脉冲微分系统有界变差解对参数的连续依赖性

文[6]讨论了比已有结果更弱的假设条件下,固定时刻一阶脉冲微分系统与Kurzweil广义常微．分方程的关系,本文在此基础之上,建立了此类脉冲微分系统有界变差解对参数的连续依赖性定理．     

Impulsive observer for input-to-state stability based synchronization of Lur’e differential inclusion system

In this paper, we consider the observer design for input-to-state stability (ISS) based synchronization of Lur’e differential inclusion system. A new impulsive observer is investigated to guarantee the error system remains bounded for any bounded disturbances. An example is employed to verify the feasibility of the designed observer.     

Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.     

Existence and Hyers-Ulam stability of random impulsive stochastic functional differential equations with finite delays

ABSTRACT

In this paper, we investigate the existence and Hyers-Ulam stability for random impulsive stochastic functional differential equations with finite delays. Firstly, we prove the existence of mild solutions to the equations by using Krasnoselskii's fixed point. Then, we investigate the Hyers-Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, an example is given to illustrate our results.     

Nonlinear impulsive systems on infinite dimensional spaces

In this paper we consider two different classes of nonlinear impulsive systems one driven purely by Dirac measures at a fixed set of points and the second driven by signed measures. The later class is easily extended to systems driven by general vector measures. The principal nonlinear operator is monotone hemicontinuous and coercive with respect to certain triple of Banach spaces called Gelfand triple. The other nonlinear operators are more regular, non-monotone continuous operators with respect to suitable Banach spaces. We present here a new result on compact embedding of the space of vector-valued functions of bounded variation and then use this result to prove two new results on existence and regularity properties of solutions for impulsive systems described above. The new embedding result covers the well-known embedding result due to Aubin.     

一类脉冲微分系统的有界变差解

在比文[6]更弱的条件下讨论了固定时刻脉冲微分系统与Kurzweil广义常微分方程的关系,并建立了这类脉冲微分系统有界变差解的局部存在性和唯一性定理．     

Mathematical model for the control of a pest population with impulsive perturbations on diseased pest

In this paper, a stage-structured pest management SI model with impulsive perturbations on infected pest is introduced. Sufficient conditions of the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of system are uniformly ultimately bounded.     

Bessel functions and singular BVPs arising in physiology in the presence of upper and lower solutions in reverse order

In this paper, we consider the genic mutation on an impulsive population system in polluted environment. All solutions of the investigated system are proved to be uniformly bounded. Using mathematical analysis methods, the conditions of the globally asymptotically stable population-extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is carried out illustrate our results. Our results provide reliable tactic basis for the practical biological resource management in polluted environment.     

非线性脉冲中立型系统输入状态稳定的一个充分条件

本文对于可测的局部本性有界输入,运用Lyapunov-Krasovskii函数方法,得到了使非线性脉冲中立型系统输入状态稳定的充分条件．     

Global attractivity and permanence of a stage-structured pest management SI model with time delay and diseased pest impulsive transmission

In this paper, we consider a stage-structured pest management SI model with time delay and diseased pests impulsive transmission. We obtain the sufficient conditions of the global attractivity of pest-extinction boundary periodic solution and the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide a reliable tactic basis for the practice of pest management.     

Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space

In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii''s fixed point theorem, the theory of evolution family and the resolvent operator. In particular,the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results.     

Mathematical Mo del for Diab etes Mellitus with Impulsive Injections of Glucose-insulin

Impulsive injections of glucose and insulin analogues are very important strate-gies for the control of diabetes mellitus. We mainly imitate diabetes patients take insulin before eating, and eating approximately as a pulse blood glucose injection, as a result, a new mathematical model with impulsive injections of both glucose and insulin at different fixed times is formulated in this paper. Using the discrete dynamical system determined by the stroboscopic map, we show that the existence and uniqueness of a positive globally asymp-totically stable periodic solution for type Ⅰ diabetes. By impulsive comparison theorem, we obtain the glucose concentration level of the system is uniformly bounded above and below for type Ⅱdiabetes. Numerical analysis verifies our theoretical results.     

Lagrange stability for impulsive Duffing equations

This work discusses the boundedness of solutions for impulsive Duffing equation with time-dependent polynomial potentials. By KAM theorem, we prove that all solutions of the Duffing equation with low regularity in time undergoing suitable impulses are bounded for all time and that there are many (positive Lebesgue measure) quasi-periodic solutions clustering at infinity. This result extends some well-known results on Duffing equations to impulsive Duffing equations.