Dynamics of a $2$-dimensional slow-fast Belousov-Zabotinsky model

Abstract: For the reduced two-dimensional Belousov-Zhabotinsky slow-fast differential system, the known results are the existence of one limit cycle and its stability for particular values of the parameters. Here, we characterize all dynamics of this system except one degenerate case. The results include global stability of the positive equilibrium, supercritical and subcritical Hopf bifurcations, the existence of a canard explosion and relaxation oscillation, and the coexistence of one nest of two limit cycles with the outer one originating from the supercritical Hopf bifurcation at one canard point and the inner one from the subcritical Hopf bifurcation at another canard point. This last one is a new dynamical phenomenon.