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Critical curves and stability region in a complex network with delayed feedback control

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  • Yang, Ping
  • Lin, Yiping

Abstract

In this paper, a two-dimensional complex network with delayed feedback control is proposed and discussed. For the network without control, the equilibrium of the network is unstable, but under the control with even very small parameters, the equilibrium of the network will become stable. A detailed stability analysis on the controlled system is provided. Differing from the previous works, on the coordinate plane of two delays, the stability region is surrounded by the critical curves. The supercritical and the subcritical Hopf bifurcations are discussed particularly along the boundary of the stability region. Numerical simulations are provided to illustrate the results. The investigation shows that there is stable region surrounded by five critical curves and there exist doubling-periodic solutions and chaotic solutions in the controlled network when the parameters keep away from the stability region. This work provides a theoretical basis for the further application of complex networks.

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  • Yang, Ping & Lin, Yiping, 2026. "Critical curves and stability region in a complex network with delayed feedback control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 548-561.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:548-561
    DOI: 10.1016/j.matcom.2025.09.011
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