Hybrid Methods for Studyng Stability and Bifurcations in Delayed Feedback Systems

Abstract

The dynamics of two related models of second order delay differential equations with four bifurcating parameters is analyzed. Through a classical technique in the time-domain which involves the location of the roots of a exponential polynomial equation, the areas of stability of the equilibrium are set. Moreover, the frequency domain methodology allows to study the Hopf bifurcation phenomena and to describe the behavior of the emerging cycles completely. Certain type of singularities, which provoke fold bifurcations of cycles are detected precisely. Also, a complete picture of resonant parameter configurations is established for both models. The whole results are checked with the software DDE-Biftool .