Exponential Synchronization of Hybrid Coupled
Networks With Delayed Coupling

Wangli He and Jinde Cao, Senior Member, IEEE

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Abstract—

This paper investigates exponential synchronization
of coupled networks with hybrid coupling, which is composed of
constant coupling and discrete-delay coupling. There is only one
transmittal delay in the delayed coupling. The fact is that in the
signal transmission process, the time delay affects only the variable
that is being transmitted from one system to another, then it makes
sense to assume that there is only one single delay contributing to
the dynamics. Some sufficient conditions for synchronization are
derived based on Lyapunov functional and linear matrix inequality
(LMI). In particular, the coupling matrix may be asymmetric or
nondiagonal. Moreover, the transmittal delay can be different from
the one in the isolated system. A distinctive feature of this work is
that the synchronized state will vary in comparison with the conventional
synchronized solution. Especially, the degree of the nodes
and the inner delayed coupling matrix heavily influence the synchronized
state. Finally, a chaotic neural network is used as the
node in two regular networks to show the effectiveness of the proposed
criteria.
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http://ieeexplore.ieeeiel5/72/5441221/05...er=5411935