Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 2, Pages 161-167

Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators

Gerold Baier and Sven Sahle

Institute for Plant Biochemistry, University of Tübingen, Tübingen D-72076, Germany

Received 9 October 1996

Copyright © 1997 Gerold Baier and Sven Sahle. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. The systems involved are: (a) a two-variable oscillator with two consecutive autocatalytic reactions derived from the Lotka–Volterra scheme; (b) a minimal two-variable oscillator with one first-order autocatalytic reaction; (c) a three-variable oscillator with first-order feedback lacking autocatalysis. The dynamics of a finite number of coupled biochemical oscillators may account for complex patterns in compartmentalized living systems like cells or tissue, and may be tested experimentally in coupled microreactors.