Existence and Spatio-Temporal Patterns of Periodic Solutions to Second Order Non-Autonomous Equivariant Delayed Systems

2020/05/26 by Balanov, Zalman, Krawcewicz, Wieslaw, Hirano, Norimichi +1
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.12558

Abstract

Existence and spatio-temporal symmetric patterns of periodic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays are studied under the Hartman-Nagumo growth conditions. The method is based on using the Brouwer D₁ × \mathbb Z₂× Γ-equivariant degree theory, where D₁ is related to the reversing symmetry, \mathbb Z₂ is related to the oddness of the right-hand-side and Γ reflects the symmetric character of the coupling in the corresponding network. Abstract results are supported by a concrete example with Γ= D_n -- the dihedral group of order 2n.

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