Period Constants and Hopf Bifurcation

The goal of this paper is to highlight the importance of certain coefficients that give a correction in the frequency of periodic solutions arising from Hopf bifurcation in dynamical systems. Those frequency coefficients are closely related to the so-called period constants found previously in the literature. The vanishing of the frequency coefficients aims at the detection and analysis of isochronous periodic solutions. The first frequency coefficients are computed for several typical examples that are well-known in the context of dynamical systems having an isochronous center. An example of a polycyclic configuration with a critical point in the period and in the amplitude is presented for illustration.