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Exponential Synchronization of the Linearly Coupled Dynamical Networks with Delays*

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Abstract

In this paper, the authors investigate the synchronization of an array of linearly coupled identical dynamical systems with a delayed coupling. Here the coupling matrix can be asymmetric and reducible. Some criteria ensuring delay-independent and delay-dependent global synchronization are derived respectively. It is shown that if the coupling delay is less than a positive threshold, then the coupled network will be synchronized. On the other hand, with the increase of coupling delay, the synchronization stability of the network will be restrained, even eventually de-synchronized.

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Authors and Affiliations

  1. Laboratory of Nonlinear Mathematics Science, School of Mathematical Sciences, Fudan University, Shang-hai, 200433, China

    Xiwei Liu

  2. Laboratory of Nonlinear Mathematics Science, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Tianping Chen

Authors
  1. Xiwei Liu
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  2. Tianping Chen
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Corresponding author

Correspondence to Tianping Chen.

Additional information

* Project supported by the National Natural Science Foundation of China (Nos. 60574044, 60774074) and the Graduate Student Innovation Foundation of Fudan University.

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Liu, X., Chen, T. Exponential Synchronization of the Linearly Coupled Dynamical Networks with Delays*. Chin. Ann. Math. Ser. B 28, 737–746 (2007). https://doi.org/10.1007/s11401-006-0194-4

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  • DOI: https://doi.org/10.1007/s11401-006-0194-4

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