Asymptotical p -Moment Stability of Stochastic Impulsive Differential Equations and Its Application in Impulsive Control

2010 ◽  
Vol 53 (1) ◽  
pp. 110-114 ◽  
Author(s):  
Niu Yu-Jun ◽  
Xu Wei ◽  
Li Hong-Wu
Keyword(s):  
Differential Equations ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Moment Stability

Pinning Impulsive Synchronization of Fractional Complex Dynamical Networks

2015 ◽  
Author(s):  
Weiyuan Ma ◽  
Changpin Li ◽  
Yujiang Wu
Keyword(s):  
Differential Equations ◽  
Comparison Principle ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Impulsive Synchronization ◽  
Pinning Impulsive Control

In this paper, a class of fractional complex dynamical networks is synchronized via pinning impulsive control. At first, a comparison principle is established for fractional impulsive differential equations. Then the synchronization criterion is obtained by using the derived comparison principle. Examples are given to illustrate the results.

Impulsive Control of Nonautonomous Chaotic Systems using Practical Stabilization

1998 ◽  
Vol 08 (07) ◽  
pp. 1557-1564 ◽  
Author(s):  
Tao Yang ◽  
Johan A. K. Suykens ◽  
Leon O. Chua
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Small Region ◽  
Asymptotic Stabilization ◽  
Practical Stabilization

In this paper, we use the concept of practical stabilization of impulsive differential equations for controlling nonautonomous chaotic systems. Instead of controlling a chaotic system to a point as in the case of asymptotic stabilization, the aim of practical control is to stabilize a chaotic system into a small region of phase space. This method is useful to control a chaotic system into a prescribed region. We present the theory of controlling a nonautonomous chaotic system into a small region around the origin and illustrate the method on Duffing's oscillator.

scholarly journals Impulsive Control Strategy for a Nonautonomous Food-Chain System with Multiple Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Baodan Tian ◽  
Yanhong Qiu ◽  
Yucai Ding
Keyword(s):  
Differential Equations ◽  
Food Chain ◽  
Impulsive Control ◽  
Control Strategies ◽  
Functional Differential Equations ◽  
Impulsive Differential Equations ◽  
Effective Control ◽  
Multiple Delays ◽  
Chain System ◽  
Holling Ii Functional Response

A nonautonomous food-chain system with Holling II functional response is studied, in which multiple delays of digestion are also considered. By applying techniques in differential inequalities, comparison theorem in ordinary differential equations, impulsive differential equations, and functional differential equations, some effective control strategies are obtained for the permanence of the system. Furthermore, effects of some important coefficients and delays on the permanence of the system are intuitively and clearly shown by series of numerical examples.

Impulsive Control and Synchronization of Nonlinear Dynamical Systems and Application to Secure Communication

1997 ◽  
Vol 07 (03) ◽  
pp. 645-664 ◽  
Author(s):  
Tao Yang ◽  
Leon O. Chua
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Secure Communication ◽  
Impulsive Control ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Impulsive Differential Equations ◽  
Channel Noise ◽  
Nonlinear Dynamical ◽  
Impulsive Synchronization

Impulsive control is a newly developed control theory which is based on the theory of impulsive differential equations. In this paper, we stabilize nonlinear dynamical systems using impulsive control. Based on the theory of impulsive differential equations, we present several theorems on the stability of impulsive control systems. An estimation of the upper bound of the impulse interval is given for the purpose of asymptotically controlling the nonlinear dynamical system to the origin by using impulsive control laws. In this paper, impulsive synchronization of two nonlinear dynamical systems is reformulated as impulsive control of the synchronization error system. We then present a theorem on the asymptotic synchronization of two nonlinear systems by using synchronization impulses. The robustness of impulsive synchronization to additive channel noise and parameter mismatch is also studied. We conclude that impulsive synchronization is more robust than continuous synchronization. Combining both conventional cryptographic method and impulsive synchronization of chaotic systems, we propose a new chaotic communication scheme. Computer simulation results based on Chua's oscillators are given.

Impulsive Control and Practical Generalized Synchronization of a Class of Uncertain Chaotic System with a Given Manifold

2015 ◽  
Vol 782 ◽  
pp. 296-301
Author(s):  
Jian Xu Ding ◽  
Cheng Wang ◽  
Yong Bi
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Coupled Systems ◽  
Generalized Synchronization

In this paper, we study practical generalized synchronization of uncertain chaotic system with a given manifold Y = H(X). We construct a class of the bi-directionally coupled chaotic systems with impulsive control, and demonstrate theoretically that the bi-coupled systems could realize practical generalized synchronization on the basis of stability theory of impulsive differential equations. Numerical simulations with super-chaotic system are provided to further demonstrate the effectiveness and generality of our approach.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

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