Search

Global bifurcation and spatio-temporal patterns of periodic solutions (with prescribed period) to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer/Leray–Schauder O (2) × Γ × ℤ 2 -equivariant degree theory. Here, O (2) is related to the reversal symmetry combined with the autonomous form of the system, Γ reflects extra spacial symmetries of the system, and ℤ 2 is related to the oddness of the right-hand side. Abstract results are supported by a concrete example with Γ = D 6 — the dihedral group of order 12. [ABSTRACT FROM AUTHOR]

The existence and spatio-temporal patterns of 2 π -periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer O (2) × Γ × Z 2 -equivariant degree theory. The solutions are supposed to take their values in a prescribed symmetric domain D, while O(2) is related to the reversal symmetry combined with the autonomous form of the system. The group Γ reflects symmetries of D and/or possible coupling in the corresponding network of identical oscillaltors, and Z 2 is related to the oddness of the right-hand side. Abstract results, based on the use of Gauss curvature of ∂ D , Hartman–Nagumo type a priori bounds and Brouwer equivariant degree techniques, are supported by a concrete example with Γ = D 8 —the dihedral group of order 16. [ABSTRACT FROM AUTHOR]