Abstract.In this paper, we analyze Hopf bifurcation phenomenon in a nonlinear small-world network model with time delay and fixing probability.By choosing time-delay as a bifurcation parameter, we obtain that the model exhibits of Hopf bifurcation when time delay passes through a critical value. In order to control the undesirable Hopf bifurcation, a time-delayed feedback control strategy is proposed. By choosing feedback parameter properly, it shows that the onset of Hopf bifurcation has been postponed without changing the original equilibrium point of the system.Finally, numerical simulations are given to verify the theoretical results.

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