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Pattern formation and spatial chaos in lattice dynamical systems. II

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2 Author(s)
J. Mallet-Paret ; Div. of Appl. Math., Brown Univ., Providence, RI, USA ; S. -N. Chow

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

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IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications  (Volume:42 ,  Issue: 10 )