Peculiarities of generalized synchronization in unidirectionally and mutually coupled time-delayed systems

In this paper, we investigate the relation between generalized and phase synchronization for time-delayed systems. Two different systems are considered, namely, Logistic and Mackey–Glass systems. Sufficient conditions for determining the generalized synchronization are derived analytically for scalar and modulated time-delay and tested for correctness by numerical simulations. We propose an example that phase synchronization is stronger than generalized synchronization for scalar time-delay and the opposite situation happens for modulated delay time.

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Nonlinear active observer-based generalized synchronization in time-delayed systems

Nonlinear Dynamics ◽

10.1007/s11071-009-9538-4 ◽

2009 ◽

Vol 59 (1-2) ◽

pp. 289-296 ◽

Cited By ~ 11

Author(s):

Dibakar Ghosh

Keyword(s):

Generalized Synchronization ◽

Delayed Systems

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Specificities of Generalized Synchronization in Delayed Systems

Technical Physics Letters ◽

10.1134/s1063785019060142 ◽

2019 ◽

Vol 45 (6) ◽

pp. 560-562 ◽

Cited By ~ 1

Author(s):

A. D. Plotnikova ◽

O. I. Moskalenko

Keyword(s):

Generalized Synchronization ◽

Delayed Systems

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Finite-time generalized synchronization of nonidentical delayed chaotic systems

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2016.3.2 ◽

2016 ◽

Vol 21 (3) ◽

pp. 306-324 ◽

Cited By ~ 33

Author(s):

Haibo Bao ◽

Jinde Cao

Keyword(s):

Finite Time ◽

Chaotic Systems ◽

Sufficient Conditions ◽

Convergence Time ◽

Generalized Synchronization ◽

Delayed Systems ◽

Finite Time Stability ◽

Control Techniques ◽

Nonlinear Control Theory ◽

Response Systems

This paper deals with the finite-time generalized synchronization (GS) problem of drive-response systems. The main purpose of this paper is to design suitable controllers to force the drive-response system realize GS in a finite time. Based on the finite-time stability theory and nonlinear control theory, sufficient conditions are derived that guarantee finite-time GS. This paper extends some basic results from generalized synchronization to delayed systems. Because finite-time GS means the optimality in convergence time and has better robustness, the results in this paper are important. Numerical examples are given to show the effectiveness of the proposed control techniques.

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