Control and coupling of spiral waves in excitable media

Abstract

We report the complex dynamics of spiral waves observed in the ferroin-catalyzed BZ reaction. The reaction is run in an open unstirred reactor (CFUR) with the catalyst immobilized on a polysulfone membrane. The catalyst-loaded membrane is placed between two well stirred compartments which are fed with solutions of sulfuric acid/malonic acid/bromide and sulfuric acid/bromate, respectively. An electrical field perpendicular to the membrane can be applied ia Pt-ring electrodes or, alternatively, ia transparent electrodes made of ITO-coated glass. In the field-free case relatively simple target and spiral patterns are observed in the membrane. If an alternating electrical field is applied the spiral core drifts through the membrane. The actual trajectory of the spiral tip depends on the amplitude and frequency of the applied electrical field. If the perturbation parameters are chosen properly the wave fronts break up and new spiral cores emerge under the influence of the alternating field. Complex spatio-temporal patterns may be induced which are reminescent of “ spiral-chaos”. After switching off the perturbation the system returns to its previous, “ simple” behaviour. Our experimental observations are confirmed by model calculations based on the Barkley model of spiral waves. The technique of using modulated excitability to control the dynamics of spiral waves is further extended to the coupling of two spirals in two CFURs. We present numerical simulations based on two identical excitable reaction–diffusion (RD) systems which are mutually coupled. The coupling is based on the observation of an arbitrarily chosen point inside each of the RD systems: If a chemical wave passes the point of optical observation in system 1 an electric field is applied to system 2 and ice ersa. Thus, a local observation made in one system is transformed in a global perturbation of the second CFUR. We report the observation of CFUR states where the two spiral waves are spatially and temporally coupled to each other.