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Symmetry-breaking and first-period-doubling following a Hopf bifurcation in a three-dimensional system. (English) Zbl 0853.70016
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.
Reviewer: H.Troger (Wien)
MSC:
70K99Nonlinear dynamics (general mechanics)
37G99Local and nonlocal bifurcation theory
34C23Bifurcation (ODE)