Stability of bifurcating periodic solutions for van der Pol equation with continuous distributed delay

摘要

The van der Pol equation with continuous distributed time delay is given. Its linear stability is investigated by employing the Routh–Hurwitz criteria. Moreover, the local asymptotic stability conditions are also derived. By using the mean time delay as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcations. The direction and the stability criteria of the bifurcating periodic solutions are obtained by applying the norm form theory and the center manifold theorem. Some numerical simulation examples for justifying the theoretical results are also given.