Forma, Vol. 4 (No. 2), pp. 75-102, 2001

Cell Dynamical Systems

Yoshitsugu Oono and Aritomo Shinozaki

Department of Physics, Materials Research Laboratory and Beckman Institute, 405 N. Mathews Ave., University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

(Received August 17, 1989; Accepted September 6, 1989)

Keywords: Space-Time Discrete Models, Cell Dynamical Systems, Nonequilibrium Phenomena, Modeling

Abstract. We illustrate the modeling of various nonlinear nonequilibrium phenomena with spatially nontrivial patterns in terms of cell dynamical systems (CDS) with the aid of phase separation kinetics, chondrogenesis, hydrodynamics, etc. CDS is a collective name for all the space-time discrete dynamical systems. Analyzing given phenomena, we directly construct CDS models. Our ultimate goal is to unravel universal mathematical structures behind various natural phenomena. Conceptual problems involved in this type of modeling are discussed in detail.