Periodic Solutions to Reversible Second Order Autonomous Systems with Commensurate Delays

Abstract

Existence and spatio-temporal patterns of periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer $O(2)\times \Gamma \times {\mathbb{Z}}_2$-equivariant degree theory, where $O(2)$ is related to the reversing symmetry, $\Gamma$ reflects the symmetric character of the coupling in the corresponding network and ${\mathbb{Z}}_2$ is related to the oddness of the right-hand-side. Abstract results are supported by a concrete example with $\Gamma =D_6$ -- the dihedral group of order 12.

arXiv admin note: text overlap with arXiv:2005.12558