Transmission of Signals via Synchronization of Chaotic Time-Delay Systems

1998 ◽  
Vol 08 (09) ◽  
pp. 1839-1842 ◽  
Author(s):  
K. Pyragas
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Secure Communication ◽  
Chaotic Synchronization ◽  
Strange Attractors ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Time ◽  
Time Signals

Secure communication via chaotic synchronization is demonstrated using dynamical systems governed by delay deferential equations. Strange attractors of such systems can have an arbitrarily large number of positive Lyapunov exponents giving rise to very complex time signals. This features can provide high security of masked messages.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

scholarly journals Study and Application of State Estimator for Time-Delay Systems with State Saturation Nonlinearities

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Yeong-Jeu Sun
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
State Estimator ◽  
State Estimate ◽  
True State ◽  
Delay Dependent ◽  
State Saturation

The design and application of state estimator for a class of time-delay systems with state saturation nonlinearities are firstly explored. Based on the Lyapunov-Razumikhin functions, delay-dependent sufficient conditions are established to guarantee the asymptotic stability of the error between the state estimate and the true state. Besides, an upper bound of arbitrary time-varying delays is derived to assure that the resulting error can converge asymptotically to zero. Finally, applications to the secure communication and simulation results are given to demonstrate the feasibility and effectiveness of the main results.

CHAOS SYNCHRONIZATION OF CHEN SYSTEMS WITH TIME-VARYING DELAYS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250183 ◽  
Author(s):  
JIANENG TANG ◽  
CAIRONG ZOU ◽  
SHAOPING WANG ◽  
LI ZHAO ◽  
PINGXIANG LIU
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Synchronization Problem ◽  
The Stability

In this paper, the synchronization problem of Chen systems with time-varying delays is discussed based on the stability theory of time-delay systems. Through the analysis of the error dynamical systems, the time-delay correlative synchronization controller is designed to achieve chaos synchronization. And finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

Synchronization of hyperchaotic harmonics in time-delay systems and its application to secure communication

2000 ◽  
Vol 62 (6) ◽  
pp. 7898-7904 ◽  
Author(s):  
Liu Yaowen ◽  
Ge Guangming ◽  
Zhao Hong ◽  
Wang Yinghai ◽  
Gao Liang
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Delay Systems ◽  
Time Delay Systems
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