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Surfaces of bifurcation in a triparametric quadratic Hamiltonian
Phys. Rev. E 52, 5540 – Published 1 November, 1995
DOI: https://doi.org/10.1103/PhysRevE.52.5540
Abstract
Numerous dynamical systems are represented by a quadratic Hamiltonian with the phase space on the sphere. In this paper, for the unique class of quadratic Hamiltonians depending on three parameters, we analyze the equilibria and the occurrence of parametric bifurcations; we obtain the surfaces of bifurcation in the space of parameters. We describe, in the context of quadratic Hamiltonians, a special type of bifurcation associated with a nonelementary fixed point; we name it a double teardrop bifurcation.
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