Kavli Affiliate: Xiang Zhang
| First 5 Authors: Ruihan Xu, Ming Sun, Xiang Zhang, ,
| Summary:
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.
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