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Bifurcation Of Limit Cycles In Smooth And Non-Smooth Dynamical Systems With Normal Form Computation, Yun Tian
Bifurcation Of Limit Cycles In Smooth And Non-Smooth Dynamical Systems With Normal Form Computation, Yun Tian
Electronic Thesis and Dissertation Repository
This thesis contains two parts. In the first part, we investigate bifurcation of limit cycles around a singular point in planar cubic systems and quadratic switching systems. For planar cubic systems, we study cubic perturbations of a quadratic Hamiltonian system and obtain 10 small-amplitude limit cycles bifurcating from an elementary center, for which up to 5th-order Melnikov functions are used. Moreover, we prove the existence of 12 small-amplitude limit cycles around a singular point in a cubic system by computing focus values. For quadratic switching system, we develop a recursive algorithm for computing Lyapunov constants. With this efficient algorithm, we …