Chemical Waves in the Oscillatory Zhabotinskii System. A Transition from Temporal to Spatio-temporal Organization

Abstract

The Zhabotinskii system [1], [2], is an excellent example of chemical synergetics [3]. When four or five chemical compounds are mixed in the appropriate concentration ranges and at the appropriate temperature, the Zhabotinskii system spontaneously organizes itself into temporal or spatio-temporal dissipative structures of macroscopic dimensions [4]. In this chemical reaction, at least twenty intermediates are formed. The chemical mechanism involved is so complex that almost all theoretical work is performed on models rather than on the best rate equations available today [5]. A first type of model involves “macrokinetic” steps rather than elementary ones. This type includes the model of ZHABOTINSKII and his collaborators [1] which attempts to reproduce both waveforms and periods of oscillations. It includes also the many versions of the Oregonator [6] which are designed to reproduce the waveforms of a few intermediates. Other models are of the heuristic-topological type, according to the PACAULT [7] classification. Two of them are the well-known PRIGOGINE-LEFEVER model [8] (or Brusselator) and the analytic BAUTIN system [9], [10] (or DREITLEIN-SMOES model). It is unnecessary to emphasize here the role played by the PRIGOGINE-LEFEVER model as a research tool in the theory of dissipative structures. The BAUTIN system is less well known in spite of several attractive features: this system is solvable in closed form; it exhibits a limit cycle and bistability; there is a saddle-node transition between steady-state and finite amplitude oscillations [2].