Secondary Bifurcation of Quasi-Periodic Solutions Can Lead to Period Multiplication

Perturbation and asymptotic methods are used to obtain the secondary bifurcation of quasi-periodic solutions from periodic solutions for a model problem. It is a two-cell model consisting of a coupled system of van der Pol-Duffing oscillators. The qualitative features of the secondary bifurcation states depends on the detuning of the oscillators. For special values of the detuning the secondary states are periodic. Then it is possible for period multiplication of solutions to occur at the secondary bifurcation point.