Nonlinearity and computation: implementing logic as a nonlinear dynamical system

Abstract Recently, Sinha and Ditto [Phys. Rev. Lett. 81 (1998) 2156] demonstrated the computational possibilities of an array of coupled maps. We generalize this nonlinear dynamical system to improve its computational usefulness. We then consider a second nonlinear system, a parameterized map, and use it to illustrate why logic requires nonlinearity.