Periodic solutions to delay differential equations with two delay via bi-Hamiltonian systems (Q2765000)

The authors establish some new sufficient criteria for the existence of periodic solutions to delay differential equations of the form NEWLINE\[NEWLINEx'(t)=-f(x(t-r_1))g(x(t-r_2))-f(x(t-r_2))g(x(t-r_1))NEWLINE\]NEWLINE and NEWLINE\[NEWLINEx'(t)=+f(x(t-r_1))g(x(t-r_2))+f(x(t-r_2))g(x(t-r_1)).NEWLINE\]NEWLINE Their approach involves the existence theory of periodic solutions to bi-Hamiltonian systems and the method of symmetry groups, which has been widely used by many authors in the literature.