Publicação: The Occurrence of Zero-Hopf Bifurcation in a Generalized Sprott A System
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2020-01-01
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From the normal form of polynomial differential systems in R3 having a sphere as invariant algebraic surface, we obtain a class of quadratic systems depending on ten real parameters, which encompasses the well-known Sprott A system. For this reason, we call them generalized Sprott A systems. In this paper, we study the dynamics and bifurcations of these systems as the parameters are varied. We prove that, for certain parameter values, the z-axis is a line of equilibria, the origin is a non-isolated zero-Hopf equilibrium point, and the phase space is foliated by concentric invariant spheres. By using the averaging theory we prove that a small linearly stable periodic orbit bifurcates from the zero-Hopf equilibrium point at the origin. Finally, we numerically show the existence of nested invariant tori around the bifurcating periodic orbit.
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Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019, p. 157-165.
