Periodic solutions of delay equations with three delays via bi-Hamiltonian systems. (English) Zbl 1101.34055

The idea of obtaining periodic solutions of delay equations from associated Hamiltonian systems of ODEs (originally due to Kaplan and Yorke) is applied to a special type of systems with three delays and enough symmetry so the method works. A kind of commensurability condition on the delays is crucial, and periodic solutions of the ODE correspond to solutions of the delay system with the same period. The role of the solutions constructed in the overall dynamics is not discussed.


34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
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