一个分数阶小世界网络模型的稳定性与Hopf分岔延迟控制

Stability and Hopf bifurcation control of a fractional-order small world network model

本文首先将一个含时滞的小世界网络模型推广到分数阶情形,然后详细讨论了其唯一正平衡点的稳定性切换与Hopf分岔,得到了稳定性区间的显式表达式和发生Hopf分岔的条件,进而采用Pyragas型时滞反馈控制,使得即使在较强非线性因素条件下,通过适当增大增益取值和调节分数阶的阶次,可显著延迟受控系统的Hopf分岔发生,从而大大提高网络系统平衡点的稳定性.数值算例验证了理论的正确性.

In this paper, a fractional-order model is firstly proposed for a small world network with time-delay, where the fractionalorder derivative is used to reflect the self-similarity of the network. Then by using the method of stability switches, the stability and Hopf bifurcation of the generalized small world network with time-delay are studied. Explicit conditions for describing the stability interval and emergence of Hopf bifurcation are obtained. Further, the Pyragas type delayed feedback control is used to delay the onset of Hopf bifurcation by increasing the gain and changing the fractional-order. Numerical examples show that the stability of the controlled system can be improved substantially.