Bifurcation analysis of spiral growth processes in plants

The formation and growth of leaves around the stem of a plant often leads t o a helical structure consisting of two counterrotating sets of spirals. Si milar arrangements (parastichies) are found for the petals, florets, stamen s, etc. of many flowers. Douady and Couder [Phys. Rev. Lett. 68, 2098 (1992 )] have demonstrated how a simple physical model involving an inhibitory in fluence on the budding process from neighboring leaves can account for the emergence of this structure. The present paper reports on a series of bifur cation analyses of that model, performed in order to examine the significan ce of different assumptions about the range of the inhibitory forces. Compu ter simulations are used to illustrate the role of transient phenomena and to determine (sections of) the basins of attraction for various coexisting structures. For certain parameter values, period-doubled structures may be observed. We also studied the intensity of fluctuations and conclude that a model based on long-range inhibition will be unable in practice to produce highly regular structures with large numbers of spirals. (C) 1999 IMACS/El sevier Science B.V. All rights reserved.