Stability and Hopf Bifurcation Analysis of Genesio System with Distributed Delays Feedback

In this paper, the Genesio system with distributed time delay feedback is studied. Its linear stability is investigated based on the Routh-Hurwitz criteria. After the local asymptotic stability is analyzed, Hopf bifurcation is demonstrated by choosing the mean time delay as a bifurcation parameter. The direction and the stability criteria of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical results.