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Hopf bifurcation of a generalized Moon–Rand system

Jaume Llibre
Organization: Universitat Autònoma de Barcelona
Department: Departament de Matemàtiques
Clàudia Valls
Organization: Universidade de Lisboa
Department: Departamento de Matemática
Journal / Anthology

Commun Nonlinear Sci Numer Simulat
Year: 2015
Volume: 20
Page range: 1070–1077

We study the Hopf bifurcation from the equilibrium point at the origin of a generalized Moon–Rand system. We prove that the Hopf bifurcation can produce 8 limit cycles. The main tool for proving these results is the averaging theory of fourth order. The computations are not difficult, but very big and have been done with the help of Mathematica and Mapple.