Symmetry-breaking and first-period-doubling following a Hopf bifurcation in a three-dimensional system (Q1905512)

The authors study symmetry breaking and period doubling of a periodic orbit following from a Hopf bifurcation in a simple three-dimensional model system of ordinary differential equations with quadratic and cubic nonlinearities. The interpretation of the problem is given as a damped linear oscillator with nonlinear feedback control. By means of the method of multiple scales a higher order approximation is constructed, the accuracy of which is compared with numerical results.