摘要 :
In this paper, we show that two concepts of h-stability and h-stability in variation for nonlinear impulsive differential systems are equivalent via t_∞-similarity of the associated variational impulsive systems and impulsive int...
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In this paper, we show that two concepts of h-stability and h-stability in variation for nonlinear impulsive differential systems are equivalent via t_∞-similarity of the associated variational impulsive systems and impulsive integral inequalities. Furthermore, we characterize h-stability for nonlinear impulsive differential systems by using the notions of piecewise continuous auxiliary functions and impulsive differential inequalities.
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This paper uses the method of linear approximation for impulsive systems and gets a theorem which guarantees a fishery model to be asymptotically stable at its equilibrium point and gives the ecological explanation.
摘要 :
The dynamics of differential system can be changed very obviously after inputting impulse signals. Previous studies show that the single chaotic system can be controlled to periodic motions using impulsive control method. It was w...
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The dynamics of differential system can be changed very obviously after inputting impulse signals. Previous studies show that the single chaotic system can be controlled to periodic motions using impulsive control method. It was well known that the dynamics of hyper-chaotic and coupled systems are very important and more complex than those of a single system. In this paper, particular impulsive control of the hyper-chaotic Lü system was proposed, which is with outer impulsive signals. It can be seen that such impulsive strategy can generate chaos from periodic orbit or control chaos to periodic orbit etc. For the first time, impulsive control induced effects on dynamics of coupled systems are considered in this paper, where the impulse effect has outer input signals. Many interesting and useful results are obtained. The coupled system can realize synchronization and its synchronization manifold can be changed with such impulsive control signals. Strict theories are given, and numerical simulations confirm the correctness of theoretical results. Keywords Impulsive differential equation - Chaotic system - Coupled systems - Impulsive control - Synchronization
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摘要 :
The dynamics of differential system can be changed very obviously after inputting impulse signals. Previous studies show that the single chaotic system can be controlled to periodic motions using impulsive control method. It was w...
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The dynamics of differential system can be changed very obviously after inputting impulse signals. Previous studies show that the single chaotic system can be controlled to periodic motions using impulsive control method. It was well known that the dynamics of hyper-chaotic and coupled systems are very important and more complex than those of a single system. In this paper, particular impulsive control of the hyper-chaotic Lu system was proposed, which is with outer impulsive signals. It can be seen that such impulsive strategy can generate chaos from periodic orbit or control chaos to periodic orbit etc. For the first time, impulsive control induced effects on dynamics of coupled systems are considered in this paper, where the impulse effect has outer input signals. Many interesting and useful results are obtained. The coupled system can realize synchronization and its synchronization manifold can be changed with such impulsive control signals. Strict theories are given, and numerical simulations confirm the correctness of theoretical results.
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In this paper, we study the uniform stability of linear delayed differential equations with impulse time windows. By means of Lyapunov functions and Razumikhin technique combined with classification discussion technique, the crite...
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In this paper, we study the uniform stability of linear delayed differential equations with impulse time windows. By means of Lyapunov functions and Razumikhin technique combined with classification discussion technique, the criterion of uniform stability is obtained, which may be used to discuss others stability of delayed differential equations with impulse time win-dows. Two examples are given to illustrate the effectiveness of the theoretic result.
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We study impulsive synchronization of two Lorenz systems. In an impulsive synchronization scheme, driving signals are transmitted to the driven system at discrete instants. The driven system changes its state variables instantaneo...
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We study impulsive synchronization of two Lorenz systems. In an impulsive synchronization scheme, driving signals are transmitted to the driven system at discrete instants. The driven system changes its state variables instantaneously at these discrete instants according to synchronization errors. An asymptotically stable impulsive synchronization scheme is presented. The boundaries of stable regions of impulsive synchronization are also presented. Computer simulation results are given. [References: 7]
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In this paper the existence of integral manifolds for impulsive differential systems with time-varying delay and with impulsive effect at fixed moments are investigated. The main results are obtained by using of piecewise continuo...
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In this paper the existence of integral manifolds for impulsive differential systems with time-varying delay and with impulsive effect at fixed moments are investigated. The main results are obtained by using of piecewise continuous Lyapunov’s functions and Razumikhin’s technique.
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In the practical application of impulsive differential systems, impulse does not always occur at the fixed-time point; it may occur in a little range of time. Namely, impulse occurs in a time window, which is more general and more...
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In the practical application of impulsive differential systems, impulse does not always occur at the fixed-time point; it may occur in a little range of time. Namely, impulse occurs in a time window, which is more general and more nearing to reality than those fixed-time impulses. Therefore, it is necessary to investigate the dynamical behaviors of impulsive differential systems with impulse time windows. In this paper, the exponential stability of these systems is researched. By means of Lyapunov functions, Razumikhin technique and other analysis methods, several novel exponential stability criteria for delayed impulsive functional differential equations with impulse time windows are obtained, which are different from the previously published results for fixed-time impulses. What is more, based on the analysis of this paper, it is worth noting that choosing an efficient impulse time window may be easier and more effective than choosing fixed-time impulsive sequences. Finally, three examples and their simulations are provided to illustrate the effectiveness of our results.
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Using successor functions and Poincaré-Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator-prey model with two state impulses is investigated. By stability theorem of periodi...
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Using successor functions and Poincaré-Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator-prey model with two state impulses is investigated. By stability theorem of periodic solution to impulsive differential equations, the stability conditions of periodic solutions to the system are given. Some simulations are exerted to prove the results.
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The present paper is devoted to the investigation of the oscillatory properties of delay parabolic systems with impulses. Some criteria are established for oscillation of the solutions of Robin boundary problems of delay parabolic...
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The present paper is devoted to the investigation of the oscillatory properties of delay parabolic systems with impulses. Some criteria are established for oscillation of the solutions of Robin boundary problems of delay parabolic differential systems with impulses.
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