Periodic solutions to reversible second order autonomous systems with commensurate delays
DOI:
https://doi.org/10.12775/TMNA.2020.039Keywords
Second order delay-differential equations, periodic solutions, commensurate delays, Brouwer equivariant degree, Burnside ring, reversible systems, equivariant systemsAbstract
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.References
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