Growing plant shoots exhibit spontaneous oscillations that Darwin observed, and termed 'circumnutations'. Recently, they have received renewed attention for the design and optimal actuation of bioinspired robotic devices. We discuss a possible interpretation of these spontaneous oscillations as a Hopf-type bifurcation in a growing morphoelastic rod. Using a three-dimensional model and numerical simulations, we analyse the salient features of this flutter-like phenomenon (e.g. the characteristic period of the oscillations) and their dependence on the model details (in particular, the impact of choosing different growth models) finding that, overall, these features are robust with respect to changes in the details of the growth model adopted. This article is part of the theme issue 'Topics in mathematical design of complex materials'.
Keywords: Hopf bifurcation; circumutations; gravitropism; morphoelastic rods.