Symmetric systems of van der Pol equations

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.