Delayed Bifurcations to Repetitive Spiking and Classification of Delay-Induced Bursting

Three new routes to repetitive spiking, i.e. the delayed transcritical bifurcation, the delayed supercritical pitchfork bifurcation and the delayed subcritical pitchfork bifurcation, are revealed in this paper. We use bifurcation theory to classify bursting patterns related to three such delayed bifurcations. Then many new bursting patterns are obtained, including 24 new bursting patterns of point-point type, 27 new bursting patterns of point-cycle type and three new bursting patterns of point-torus type. Our study suggests that the classification of bursting remains to be further explored, since many new bursting patterns may be obtained based on new routes to repetitive spiking, even though we just consider codimension-1 bifurcations.

Stirring Effect on the Belousov-Zhabotinsky Oscillating Chemical Reactions in a Batch. Experimental and Modelling

We have studied the stirring effect on the time-delayed bifurcations of transient oscillations in the Belousov-Zhabotinsky (BZ) oscillating chemical reaction in a closed system. Experiments show that oscillations disappear through the time-delayed Hopf bifurcations, whose parameters depend on the stirring rate. The explanation of the stirring effect is based on the theories of diffusion-controlled reactions and hydrodynamic turbulence. We show that an increase of the stirring rate leads to an increase of the rate constant for the diffusion-controlled reaction. We propose a kinetic scheme that describes the effect observed in the experiments. A good agreement between the experimental data and the simulations is obtained.