一类带有Holling Ⅱ类功能性反应和相互干扰及脉冲效应的捕食系统

A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.     

带有脉冲控制的生物系统种群持久存在性问题研究

In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,small amplitude perturbation skills and compar-ison technique,we get the condition which guarantees the global asymptotical stability of the prey-x-eradication and predator-y-eradication periodic solution.It is proved that the system is permanent.Furthermore,numerical simulations are also illustrated which agree well with our theoretical analysis.All these results may be useful in study of the dynamic complexity of ecosystems.     

PERMANENCE OF A NON-AUTONOMOUS BEDDINGTON-DEANGELIS PREDATOR-PREY MODEL WITH TIME DELAY AND IMPULSIVE CONTROLS

A non-autonomous predator-prey delay system with Beddington-DeAngelis functional response and impulsive controls is established. A set of sufficient conditions which guarantee the prey and the predator to be permanent are obtained.     

APPROXIMATE CONTROLLABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND INFINITE DELAY

This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.     

一类具有脉冲注射葡萄糖——胰岛素的糖尿病模型（英文）

Impulsive injections of glucose and insulin analogues are very important strategies 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 asymptotically 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 Ⅱ diabetes. Numerical analysis verifies our theoretical results.     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.     

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.     

PERIODIC SOLUTION TO PREDATOR-PREY CHAIN SYSTEM WITH IMPULSIVE EFFECTS AND BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE

In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.     

Boundedness of Nonlinear Differential Systems with Impulsive Effect on Random Moments

The model of nonlinear differential systems with impulsive effect on random moments is broughtforward in this paper.Then,sufficient conditions for(uniform,uniform and ultimate,and uniform and uniformlyultimate) p-moment boundedness of the systems are presented.Finally,an example is discussed to showapplications of two obtained results.     

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.     

具有脉冲扰动和非单调功能反应的三种群捕食系统的分析

研究一类具有脉冲效应和非单调功能反应的两个捕食者一个食饵害虫控制系统．通过脉冲微分方程的Floquet理论和小幅扰动方法,证明了当脉冲周期小于某个临界值时,系统存在一个渐近稳定的害虫根除周期解,否则系统是持续生存的．最后,通过数值实例,给出了一简单讨论．     

一类具脉冲效应的三种群捕食系统的动力学性质

基于综合害虫管理,提出并研究了一类具有脉冲效应和Holling Ⅱ类功能反应的两个捕食者一个食饵系统.利用脉冲微分方程的Floquet理论和比较定理,得到了系统灭绝和持续生存的充分条件.最后,简要讨论了该综合害虫管理策略的有效性及系统在周期脉冲扰动下的动力复杂性.     

Permanence in a periodic delay logistic system subject to constant impulsive stocking

In this paper, a periodic impulsive delay single population system with hereditary effect is established. The constant impulse is realized at fixed moments of time. By using the comparison principle of impulsive differential equations and analysis techniques, the permanence of the system is obtained. It shows that the constant impulsive stocking plays an important role. Numerical simulations are presented to substantiate our analytical results. Copyright © 2009 John Wiley & Sons, Ltd.     

具脉冲效应的非自治随机干扰的捕食-食饵系统的研究

建立一个具有脉冲效应的非自治随机的比例依赖的捕食-食饵模型,通过研究具有脉冲效应的非自治随机系统与无脉冲效应的非自治随机系统的等价性,证明该模型的有界性,均值一致有界和灭绝性等动力学性质.     

Bifurcation of a three molecular saturated reaction with impulsive input

Although impulsive differential equations have become a widely concerned subject and a lot of models with impulsive effect have been studied in recent years, biochemical reaction models with impulsive input are rarely studied. In this paper, we consider an irreversible three molecular reaction model with impulsive input. By using the Floquet theorem and the method for the small parameter of impulsive differential equations, we obtain sufficient conditions for asymptotical stability and global stability of the given system. The existence of a positive periodic solution is also studied by the bifurcation theory. Further, we also show that our given conditions are right by numerical simulations.     

具有脉冲效应的两食饵一捕食者系统分析

构建并分析了一个在固定时刻脉冲投放捕食者且具有功能性反应的两食饵一捕食者系统,应用脉冲比较定理和微分方程的分析方法,得到了食饵灭绝周期解稳定的条件和系统持续生存的条件,并数值分析了所得的理论结果.     

Continuous approximation of linear impulsive systems and a new form of robust stability

The time-scale tolerance for linear ordinary impulsive differential equations is introduced. How large the time-scale tolerance is directly reflects the degree to which the qualitative dynamics of the linear impulsive system can be affected by replacing the impulse effect with a continuous (as opposed to discontinuous, impulsive) perturbation, producing what is known as an impulse extension equation. Theoretical properties related to the existence of the time-scale tolerance are given for periodic systems, as are algorithms to compute them. Some methods are presented for general, aperiodic systems. Additionally, sufficient conditions for the convergence of solutions of impulse extension equations to the solutions of their associated impulsive differential equation are proven. Counterexamples are provided.     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.     

Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations

The effect of periodic forcing and impulsive perturbations on predator–prey model with Holling type IV functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbations are affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade.     

Exponential stability of nonlinear state-dependent delayed impulsive systems with applications

The exponential stability problem for impulsive systems subject to double state-dependent delays is studied in this paper, where state-dependent delay (SDD) is involved in both continuous dynamics and discrete dynamics and the boundedness of it with respect to states is prior unknown. According to impulsive control theory, we present some Lyapunov-based sufficient conditions for the exponential stability of the concerned system. It is shown that the stabilizing effect of SDD impulses on an unstable SDD system changes the stability and achieves desired performance. In addition, the destabilizing effect of SDD impulses is also fully considered and the corresponding sufficient conditions are derived, which reveals the fact that a stable SDD system can maintain its performance when it is subject to SDD impulsive disturbance. As an application, the proposed result can be employed to the stability analysis of impulsive genetic regulatory networks (GRNs) with SDD and the corresponding sufficient conditions are proposed in terms of the model transformation technique and the linear matrix inequalities (LMIs) technique. In order to demonstrate the effectiveness and applicability of the derived results, we give two examples including impulsive GRNs with SDD and the impulsive controller design for the nonlinear system with SDD.