Synchronization Between Adaptively Coupled Systems With Discrete and Distributed Time-Delays

This paper investigates complete synchronization of unidirectionally and adaptively coupled systems with discrete and distributed time delays. Instead of the conventional hypothesis of a uniform Lipschitz condition on the system's vector fields, only a local Lipschitz condition is adopted. It i...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2010-04, Vol.55 (4), p.819-830
Main Authors: Lin, Wei, Ma, Huanfei
Format: Article
Language:English
Subjects:
Adaptive coupling
Applied sciences
Complex networks
Computational systems biology
Computer science
Computer science
control theory
systems
control
Control theory. Systems
Convergence
Couplings
Delay
Delay effects
Delay systems
Exact sciences and technology
Kinetic theory
Lipschitz condition
locally Lipschitzian
Mathematical analysis
Studies
Synchronism
Synchronization
System theory
Time delay
Time varying systems
time-delays
Vectors (mathematics)
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Description
Summary:This paper investigates complete synchronization of unidirectionally and adaptively coupled systems with discrete and distributed time delays. Instead of the conventional hypothesis of a uniform Lipschitz condition on the system's vector fields, only a local Lipschitz condition is adopted. It is proved that the local complete synchronization can be achieved through a unidirectional and adaptive coupling, and that the global complete synchronization can be realized when the nonlinear degree of the vector fields is smaller than some derived critical value. The results are illustrated in some representative models with time delays. Also considered is complete synchronization with an exponential convergence rate on the adaptively coupled time-delayed systems with vector fields that are one-sided uniformly Lipschitz (systems of this type can admit time-varying discrete and distributed delays). All the results can be further generalized to various types of synchronization between bidirectionally coupled time-delayed systems or among delayed kinetic systems of a complex network.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2010.2041993