Bifurcations of cycles in the unfoldings of singularities using harmonic balance

F. I. ROBBIO; J. L. MOIOLA; D. M. ALONSO

Shangai

Congreso; Shanghai International Symposium on Nonlinear Science and Applications; 2003

Research Center for Nonlinear Science of Fudan University and the Shanghai Society of Biophysics

Bifurcations of limit cycles close to certain singularities of the vector fields are explored in this paper using the harmonic balance method and the theory of nonlinear feedback systems. Perioddoubling, pitchfork and Neimark-Sacker bifurcations of cycles are computed in the parameter plane. This computation is performed in the vicinity of a singularity which has a zero eigenvalue and an imaginary pair of complex eigenvalues in the linearization of the flow around its equilibrium. A couple of 3-dimensional dynamical systems, named modified Rössler systems for brevity, with quadratic and cubic nonlinearities are used to show the main results.