Periodic bursting oscillations involving stick-slip motions as well as the generation mechanism in a Filippov-type slow–fast dynamical system

By taking a low-frequency excited modified Chua's circuit model with discontinuous vector field as an academic example, this paper introduces the periodic bursting patterns characterised by stick-slip motions as well as the underlying generation mechanism uniquely belonging to Filippov-type slow-fast dynamical systems (FSFDSs). Based on the tangencies and the visibilities, this paper is the first to clearly explain the unique transition routes to bursting phenomena involving stick-slip motions by introducing the subdivisions of the sliding region. The results indicate that such transition routes are heavily dependent on the local structures of pseudoequilibrium (PE), performing distinct non-conventional bifurcation schemes. Furthermore, two transition routes respectively corresponding to a stable node-type PE and a stable focus-type PE as well as the induced periodic bursting oscillations are further discussed in numerical simulations. Particularly, it should be pointed out that the second one is a novel route to bursting oscillation in FSFDSs. (author)