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

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  • Valls, Claudia

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.

Suggested Citation

  • Valls, Claudia, 2015. "Center problem in the center manifold for quadratic and cubic differential systems in R3," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 180-191.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:180-191
    DOI: 10.1016/j.amc.2014.11.057
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