Nonlinearity and computation: implementing logic as a nonlinear dynamical system

Recently, Sinha and Ditto [Phys. Rev. Lett. 81 (1998) 2156] demonstrated th e computational possibilities of an array of coupled maps. We generalize th is nonlinear dynamical system to improve its computational usefulness. We t hen consider a second nonlinear system, a parameterized map, and use it to illustrate why logic requires nonlinearity. (C) 1999 Elsevier Science B.V. All rights reserved.