Exact number of limit cycles for a family of rigid systems

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For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condition that allows us to separate the existence and the nonexistence of limit cycles can be described, it is very intricate. © 2004 American Mathematical Society.
Original languageEnglish
Pages (from-to)751-758
JournalProceedings of the American Mathematical Society
Publication statusPublished - 1 Mar 2005


  • Bifurcation
  • Limit cycle
  • Rigid system
  • Rotated vector field


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