Lower bounds for the cyclicity of centers of quadratic three-dimensional systems - Gouveia, Luiz F.S. [UNESP]; Queiroz, Lucas [UNESP] (Elsevier, 2024)
We consider quadratic three-dimensional differential systems having a Hopf singular point. We study their 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, including the Rössler, Lorenz, and Moon-Rand systems. Moreover, we construct an example of a jerk system to obtain 12 limit cycles bifurcating from the center, which is a new lower bound for three-dimensional quadratic systems.
Keywords: Bifurcation; Center problem; Cyclicity; Hopf singularities; Lyapunov constants