Disconnected synchronized regions of complex dynamical networks

Details Disconnected synchronized regions of complex dynamical networks Disconnected synchronized regions of complex dynamical networks

2007-06-20

arxiv.org/abs/0706.2899v1

Mathematics

Combinatorics

13 pages, 2 figures

Scientific paper

This paper addresses the synchronized region problem, which is reduced to a matrix stability problem, for complex dynamical networks. For any natural number $n$, the existence of a network which has $n$ disconnected synchronized regions is theoretically demonstrated. This shows the complexity in network synchronization. Convexity characteristic of stability for matrix pencils is further discussed. Smooth and generalized smooth Chua's circuit networks are finally discussed as examples for illustration.

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