On occurrence of mixed-torus bursting oscillations induced by non-smoothness

The paper devotes to the slow–fast behaviors of a higher-dimensional non-smooth system with coupling two scales. Some novel bursting attractors and interesting phenomena are presented, especially so-called mixed-torus oscillations, in which trajectory moves along different tori turn, though attractor still behaves quasi-periodic form. Based on 4-D hyper-chaotic model scrolls, modified version is established. Upon smooth bifurcations analysis, coexisted variation slow-varying parameter derived. With increase exciting amplitude, oscillations may change from periodic attractor, mechanism obtained by employing overlap transformed phase portrait as well bifurcations. Sliding boundary can be observed accounted for theory or in-turn influence pseudo-attractors regions. Super-cone defined an unstable focus lead period-adding period-decreasing spiking while fold limit cycle bifurcation result dramatical amplitude. Different cycles involve full vector field, resulting quiescent states seem pivots oscillations.