Lower bounds for the cyclicity of centers of quadratic three-dimensional systems
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Abstract
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.
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Bifurcation, Center problem, Cyclicity, Hopf singularities, Lyapunov constants
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English
Citation
Journal of Mathematical Analysis and Applications, v. 530, n. 1, 2024.
