Sunflower model: time-dependent coefficients and topology of the periodic solutions set

We investigate the structure of the set of periodic solutions of a time-dependent generalized version of the sunflower equation (in fact of the delayed Liénard equation), where the coefficients can vary periodically, thus allowing for environmental oscillations. Our result stems from a more general analysis, based on fixed point index and degree-theoretic methods, of the set of T-periodic solutions of T-periodically perturbed coupled delay differential equations on differentiable manifolds.