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

Abstract

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.