Symmetric systems of Van Der Pol equations

Zolman Balanov, Meymanat Farzamirad, Wiesław Krawcewicz

DOI: http://dx.doi.org/10.12775/TMNA.2006.002

Abstract


We study the impact of
symmetries on the occurrence of periodic solutions in systems of
van der Pol equations. We apply the equivariant
degree theory to establish existence results for multiple nonconstant
periodic solutions and classify their symmetries. The computations of the
algebraic invariants in the case of dihedral, tetrahedral, octahedral and
icosahedral symmetries for a van der Pol system of equations are included.

Keywords


Equivariant degree; primary degree; basic degree; dihedral; tetrahedral; octahedral and icosahedral symmetry group; van der Pol systems of non-linear oscillators; periodic solutions; topological classification of symmetric periodic solutions

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