Periodic solutions of systems of ordinary differential equations which approximate delay equations (Q752295)

We study a very simple approximation scheme for \[ (1)\quad \dot x(t)=- \alpha f(x(t-1)),\quad t\geq 0,\quad x(t)=\phi (t),\quad -1\leq t\leq 0, \] where \(\alpha >0\) and f:R\(\to R\), and demonstrate that the approximating ordinary differential systems inherit from (1) the occurence of Hopf bifurcations and the existence of global branches of nontrivial periodic solutions.