Abstract
In this paper, a fractional-order model is firstly proposed for a small world network with time-delay, where the fractional-order 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.
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