COEXISTENCE OF MULTIPLE PROPAGATING WAVE-FRONTS IN A REGULATED ENZYMEREACTION MODEL - LINK WITH BIRHYTHMICITY AND MULTITHRESHOLD EXCITABILITY

We analyze the spatial propagation of wave-fronts in a biochemical mod el for a product-activated enzyme reaction with non-linear recycling o f product into substrate. This model was previously studied as a proto type for the coexistence of two distinct types of periodic oscillation s (birhythmicity), The system is initially in a stable steady state ch aracterized by the property of multi-threshold excitability, by which it is capable of amplifying in a pulsatory manner perturbations exceed ing two distinct thresholds. In such conditions, when the effect of di ffusion is taken into account, two distinct wave-fronts are shown to p ropagate in space, with distinct amplitudes and velocities, for the sa me set of parameter values, depending on the magnitude of the initial perturbation. Such a multiplicity of propagating wave-fronts represent s a new type of coexistence of multiple modes of dynamic behavior, bes ides the coexistence involving, under spatially homogeneous conditions , multiple steady states, multiple periodic regimes, or a combination of steady and periodic regimes. (C) 1998 Elsevier Science B.V. All rig hts reserved.