scholarly journals p-moment stability of stochastic impulsive differential equations and impulsive synchronization of Lorenz system excited by parameter white-noise

2009 ◽  
Vol 58 (5) ◽  
pp. 2983
Author(s):  
Niu Yu-Jun ◽  
Xu Wei ◽  
Rong Hai-Wu ◽  
Wang Liang ◽  
Feng Jin- Qian
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Lorenz System ◽  
Impulsive Differential Equations ◽  
Impulsive Synchronization ◽  
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.

p-moment stability of stochastic impulsive differential equations and its application in impulsive control

2009 ◽  
Vol 52 (3) ◽  
pp. 782-786 ◽  
Author(s):  
Wei Xu ◽  
YuJun Niu ◽  
HaiWu Rong ◽  
ZhongKui Sun
Keyword(s):  
Differential Equations ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Moment Stability

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.

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.

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

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