On the hyperbolicity of rapidly oscillating periodic solutions of functional differential equations (Q2571494)

Consider the equation \[ x'(t)=-\mu x(t)+f(x(t-1)),\tag{1} \] where \(\mu>0\) and \(f:\mathbb{R}\to \mathbb{R}\) is an odd continuously differentiable function such that \(f(y)>0\) for \(y>0\). The problem of hyperbolicity of a periodic solution of (1) with rational period less than 2 is studied.