Bifurcation analysis of spiral growth processes in plants

The formation and growth of leaves around the stem of a plant often leads to a helical structure consisting of two counterrotating sets of spirals. Similar arrangements (parastichies) are found for the petals, florets, stamens, etc. of many flowers. Douady and Couder [Phys. Rev. Lett. 68, 2098 (1992)] have demonstrated how a simple physical model involving an inhibitory influence on the budding process from neighboring leaves can account for the emergence of this structure. The present paper reports on a series of bifurcation analyses of that model, performed in order to examine the significance of different assumptions about the range of the inhibitory forces. Computer 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/Elsevier Science B.V. All rights reserved.