Dynamical models of phyllotaxis

Leave patterns on plants (phyllotaxis) present remarkable universal feature s. The underlying morphogenesis phenomenon can be modelled by a class of dy namical systems referred to as inhibitory field models. Numerical studies h ave shown that, surprisingly often, the fixed points of such systems closel y 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 particu lar to the model of Thornley. But the analysis is general enough to embrace all models usually considered: an explicit criterion is given to explain u nder which circumstances noble numbers are actually selected. A stability a nalysis of the fixed points is also performed, explaining observed bifurcat ions. (C) 2001 Elsevier Science B.V. All rights reserved.