Bifurcation Analysis of a Nfde Arising from Multiple-Delay Feedback Control

We study the stability and Hopf bifurcation of a neutral functional differential equation (NFDE) which is transformed from an amplitude equation with multiple-delay feedback control. By analyzing the distribution of the eigenvalues, the stability and existence of Hopf bifurcation are obtained. Furthermore, the direction and stability of the Hopf bifurcation are determined by using the center manifold and normal form theories for NFDEs. Finally, we carry out some numerical simulations to illustrate the results.

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