S. Lubkin, UNIDIRECTIONAL WAVES ON RINGS - MODELS FOR CHIRAL PREFERENCE OF CIRCUMNUTATING PLANTS, Bulletin of mathematical biology, 56(5), 1994, pp. 795-810
Twining plants exhibit a striking oscillation of their stems in their
quest for a support. The oscillations, called circumnutation, have per
iods generally of 1-5 hr, and virtually all species have a preferred d
irection of twining. I seek to explain these chiral asymmetries in pla
nt behavior by hypothesizing a chiral asymmetry in plant anatomy. Such
asymmetries already exist, for example, in phyllotaxis. I explore wav
e phenomena on asymmetric but isotropic rings, and seek systems which
will only support (stable) waves in one direction around the ring, and
not in the other. Simulations indicate that (1) oscillatory reaction-
diffusion systems do not support unidirectional waves on rings; (2) ex
citable reaction-diffusion systems do support unidirectional waves on
rings. and (3) unidirectional phase-locking (discrete unidirectional w
aves) occurs in rings of coupled oscillators. Thus, chiral asymmetries
of circumnutating plants cannot be explained by continuum oscillator
phenomena, but can be explained by general discrete oscillators, or ex
citable phenomena on the continuum.