Abstract

LI, Shaowen; LIAO, Xiaofeng  and  LI, Shaorong. Frequency domain approach to Hopf bifurcation for van der Pol equation with distributed delay. Lat. Am. appl. res. [online]. 2004, vol.34, n.4, pp.267-274. ISSN 0327-0793.

The van der Pol equation with a distributed time delay and a strong kernel is analyzed. Its linear stability is investigated by employing the generalized Nyquist stability and Routh-Hurwitz criteria. Moreover, local asymptotic stability conditions are also derived in the case of the strong kernel. 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 the graphical Hopf bifurcation theory. Some numerical simulation examples for justifying the theoretical analysis are also given.

Keywords : Van der Pol Equation; Distributed Delay; Hopf Bifurcation; Periodic Solutions; A Polycyclic Configuration.

        · text in English     · English ( pdf )