Pattern formation and spatial chaos in lattice dynamical systems.II

摘要

For part I see ibid., vol.42, no.10, pp.746-51 (1995). We survey a class of continuous-time lattice dynamical systems, with an idealized nonlinearity. We introduce a class of equilibria called mosaic solutions, which are composed of the elements 1, -1, and 0, placed at each lattice point. A stability criterion for such solutions is given. The spatial entropy h of the set of all such stable solutions is defined, and we study how this quantity varies with parameters. Systems are qualitatively distinguished according to whether h=0 (termed pattern formation), or h>0 (termed spatial chaos). Numerical techniques for calculating h are described