Center problem in the center manifold for quadratic and cubic differential systems in R3

Claudia Valls

Applied Mathematics and Computation, 2015, vol. 251, issue C, 180-191

Abstract: We obtain necessary and sufficient conditions for the existence of a center on a local center manifold for three six-parameter families of quadratic systems on R3. We also give a positive answer to the conjecture posed in Mahdi (2013) for a special class of systems, called the Moon–Rand systems in the particular case when λ=2 and f is a homogeneous cubic polynomial. We also solve the center problem for a natural generalization of the above mentioned Moon–Rand systems.

Keywords: Center–focus problem; Center manifolds; First integrals (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:180-191

DOI: 10.1016/j.amc.2014.11.057

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