A 3-VARIABLE MODEL OF DETERMINISTIC CHAOS IN THE BELOUSOV-ZHABOTINSKY REACTION

CHAOS is exhibited by a wide variety of systems governed by nonlinear dynamic laws 1-3. Its most striking feature is an apparent randomness which seems to contradict its deterministic origin. The best-studied chaotic chemical system is the Belousov-Zhabotinsky (BZ) reaction 4-6 in a continuous-flow stirred-tank reactor (CSTR). Here we present a simple mechanism for the BZ reaction which allows us to develop a description in terms of a set of differential equations containing only three variables, the minimum number required to generate chaos in a continuous (non-iterative) dynamical system 2. In common with experiments, our model shows aperiodicity and transitions between periodicity and chaos near bifurcations between oscillatory and steady-state behaviour, which occur at both low and high CSTR flow rates. While remaining closely related to a real chaotic chemical system, our model is sufficiently simple to allow detailed mathematical analysis. It also reproduces many other features of the BZ reaction better than does the simple Oregonator 7 (which cannot produce chaos).