3D HYPERCYCLES HAVE NO STABLE SPATIAL STRUCTURE

Two-dimensional (2D) hypercycles have been shown to generate spiral pa tterns, which may protect the hypercycle from parasites that would be fatal to the hypercycle in a homogeneous spatial distribution. We perf orm numerical experiments on a partial differential equations hypercyc le model and show that scroll rings are formed and are not stable: The y contract by a power law and disappear within finite time. Similar re sults are obtained with a 3D cellular automaton hypercycle model. For the 3D hypercycle the final state is homogeneously oscillating, except with initial conditions creating plane waves or 2D spirals. This indi cates that the mechanism which may protect the 2D hypercycle from para sites is not applicable to 3D hypercycles. The contraction of the scro ll rings is analogous to what has been observed and calculated for oth er phenomena and models, of which one is the Belousov-Zhabotinsky reac tion, described by several mathematical models.