The main purpose of this paper is to study point-cycle type bistability as well as induced periodic bursting oscillations by taking a modified Filippov-type Chua's circuit system with a low-frequency external excitation as an example. Two different kinds of bistable structures in the fast subsystem are obtained via conventional bifurcation analyses; meanwhile, nonconventional bifurcations are also employed to explain the nonsmooth structures in the bistability. In the following numerical

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... gations, dynamic evolutions of the full system are presented by regarding the excitation amplitude and frequency as analysis parameters. As a consequence, we can find that the classification method for periodic bursting oscillations in smooth systems is not completely applicable when nonconventional bifurcations such as the sliding bifurcations and persistence bifurcation are involved; in addition, it should be pointed out that the emergence of the bursting oscillation does not completely depend on bifurcations under the point-cycle bistable structure in this paper. It is predicted that there may be other unrevealed slow–fast transition mechanisms worthy of further study.