Lower bounds for the cyclicity of centers of quadratic three-dimensional systems

2021/10/25 by Gouveia, Luiz F. S., Queiroz, Lucas
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.13255

Abstract

We consider quadratic three-dimensional differential systems having a Hopf singular point. We study the cyclicity when the singular point is a center on the center manifold using higher order developments of the Lyapunov constants. As a result, we make a chart of the cyclicity by establishing the lower bounds for several known systems in the literature, among them the Rossler, Lorenz and Moon-Rand systems. Moreover, we obtain an example of a jerk system for which is possible to bifurcate 12 limit-cycles from the center, which is a new lower bound for three-dimensional quadratic systems.

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