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Synchronization and control for directed and multiweighted networks with multiple time delays

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  • Liu, Xiwei
  • Liu, Weijin
  • Wang, Lili

Abstract

Synchronization and control problem of directed and multiweighted complex networks with multiple time delays has been studied in this paper. Entanglement between time delays and directed coupling makes the synchronization and pinning control analysis a great challenge. As for the irreducible and asymmetric coupling matrices, we prove that if their left eigenvectors corresponding to the zero eigenvalue are close enough, then they all can play a positive rule for synchronization. On the other hand, if the coupling matrices are reducible, then we can weight them together by using the elements of inner coupling matrices into union matrices for synchronization, so the interactive relationships between nodes are allowed to be cooperative and competitive. Moreover, as for the time delays, they can be unbounded and non-differentiable, and we use the maximum-value function method to measure and discuss the corresponding synchronization speed. Furthermore, we propose two novel adaptive rules to keep the synchronization speed. Finally, the correctness and validity of obtained sufficient conditions are verified by numerical simulations.

Suggested Citation

  • Liu, Xiwei & Liu, Weijin & Wang, Lili, 2026. "Synchronization and control for directed and multiweighted networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 205(C).
    • Handle: RePEc:eee:chsofr:v:205:y:2026:i:c:s0960077926000329
    DOI: 10.1016/j.chaos.2026.117891
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