Dynamical models of phyllotaxis

Leave patterns on plants (phyllotaxis) present remarkable universal features. The underlying morphogenesis phenomenon can be modelled by a class of dynamical systems referred to as inhibitory field models. Numerical studies have shown that, surprisingly often, the fixed points of such systems closely correspond to noble numbers; this is exactly what is observed in nature. In the present paper a proof of this fact is given, that applies in particular to the model of Thornley. But the analysis is general enough to embrace all models usually considered: an explicit criterion is given to explain under which circumstances noble numbers are actually selected. A stability analysis of the fixed points is also performed, explaining observed bifurcations.