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The control gain region for synchronization in non-diffusively coupled complex networks

Author

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  • Gequn, Liu
  • Wenhui, Li
  • Huijie, Yang
  • Knowles, Gareth

Abstract

The control gain region for synchronization of non-diffusively coupled networks was studied with respect to three conditions: synchronization, synchronization in finite time, and synchronization in the minimum time. Based on cancellation control methodology and master stability function formalism, we found that a complete feasible control gain region may be bounded, unbounded, empty or a union of several bounded and unbounded regions, with a similar shape to the synchronized region. An interesting possibility emerged that a network could be synchronized by both negative and positive feedback control simultaneously. By bridging synchronizability and synchronizing response speeds with a settling time index, we have developed timed synchronized region (TSR) as a substitute for the classical synchronized region to study finite time synchronization. As for the last condition, a graphical method was developed to estimate control gain with the minimum synchronization time (CGMST). Each condition has examples provided for illustration and verification.

Suggested Citation

  • Gequn, Liu & Wenhui, Li & Huijie, Yang & Knowles, Gareth, 2014. "The control gain region for synchronization in non-diffusively coupled complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 17-24.
    • Handle: RePEc:eee:phsmap:v:405:y:2014:i:c:p:17-24
    DOI: 10.1016/j.physa.2014.02.012
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