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Published on: July 15, 2014
Cluster lag synchronization and control for multiplex and directed network systems
1School of Information and Intelligent Science, Donghua University, Shanghai 201620, China; Department of Computer Science and Technology, and the Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai 201804, China; Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
None:
This article addresses cluster lag synchronization (CLSyn) and control problems for multiplex and directed network systems (MDNS). Outer matrices (OMs) of the presented model can be directed, with competitive elements, and even not connected. Additionally, inner matrices containing negative elements are used for CLSyn, which significantly improves existing results. First, a concept of CLSyn is proposed encompassing both cluster complete synchronization and cluster anticipated synchronization. Then, we study CLSyn and cluster anticipated synchronization for MDNS under a coupling agreement with time lags by employing a rearranging variable order technique. Moreover, synchronization rules under pinning control and adaptive strength are derived. Furthermore, CLSyn and pinning control conditions are established for multiplex and directed reaction-diffusion network systems (MDRDNS) as an application. Finally, simulations of MDRDNS are provided using a two step Richtmyer algorithm with the Crank-Nicolson scheme, to verify the validity of these obtained results.
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