Naimark-Sacker bifurcations in the Euler method for a delay differential equation (Q1283251)

This paper deals with an application of the Euler method to the equation \(u'(t)=-\mu u(t-1)(1-u^2(t))\), \(\mu>0\), which has a Hopf bifurcation at \(\mu=\pi/2\). The author proves that such bifurcations occur in the discretization by using the center manifold theorem and the Naimark-Sacker theorem [cf. \textit{G. Iooss}, Bifurcation of maps and applications, North-Holland, Amsterdam (1979; Zbl 0408.58019)].