Chemical Turbulence: Chaos in a Simple Reaction-Diffusion System

Abstract

Nonperiodic oscillation (“chaos”), formerly found in several 3-variable homogeneous abstract reaction systems, is also possible in 2-morphogen compartmental systems. In a 2-cellular (and hence 4-variable) symmetrical morphogenetic system of Rashevsky-Turing type, a nonperiodic return toward an (almost) undifferentiated state is observed under numerical simulation. The system hereby shows a novel, “bichaotic” (rather than bistable), type of behavior. The 2 chaotic regimes are of the screw type each. They are separated by a symmetrical saddle-limit cycle. This behavior is preserved under a “contraction” of the system to 3 variables. A second bichaotic mode (2 spiral type chaotic regimes separated by a symmetrical steady state) is also possible. A preliminary result on a third of chaos is also presented. Thus, “turbulence” (or chaos) may be a general behavioral possibility of interaction-type morphogenetic systems. © 1976, Walter de Gruyter. All rights reserved.