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Analysis on bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system. (English) Zbl 1134.70010

Summary: We examine bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system. The original mechanical system is first transformed to a Cartesian averaged equation, which is in the form of a \(Z_{2}\)-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, using the bifurcation theory of planar dynamical system and the method of detection function, the bifurcations of multiple limit cycles of the system are investigated and the configurations of compound eyes are obtained.

MSC:

70K50 Bifurcations and instability for nonlinear problems in mechanics
70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics
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