Hopf bifurcation of sunflower equation parametrized by delay (Q1902255)

The authors consider the sunflower equation \[ \ddot \alpha + \left( {a \over r} \right) \dot \alpha + \left( {b \over r} \right) \sin \alpha (t - r) = 0. \tag{1} \] Considering \(r\) as a bifurcation parameter, they prove that (1) admits a Hopf bifurcation when \(r\) is close to \(r_0 = a \omega_0/b \sin \omega_0\) where \(\omega_0\) is the unique solution of the equation \(\tan \omega = a/ \omega\) on the interval \((0, \pi/2)\). In addition, making use of an algorithm given by \textit{N. D. Kazarinoff}, \textit{Y.-H. Wan} and \textit{P. van den Driessche} [J. Inst. Math. Appl. 21, 461-477 (1978; Zbl 0379.45021)], they show that the bifurcation is supercritical, and the bifurcating periodic solutions are orbitally asymptotically stable with asymptotic phase.