Back to Search
Start Over
Bursting oscillations with a codimension-2 non-smooth bifurcation in a piecewise-smooth system of Filippov type.
- Source :
-
Chaos, Solitons & Fractals . Jul2024, Vol. 184, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- This paper focus on the effects of a codimension-2 non-smooth bifurcation on bursting behaviors in piecewise-smooth systems. A passive circuit with a switched power source is slightly modified by introducing a periodic exciting voltage to establish an example system of Filippov-type. By using Filippov's convex method, the sliding vector field is obtained, and the analytical solution of the sliding motion equation is derived. A codimension-2 non-smooth bifurcation, called "catastrophic boundary focus and catastrophic crossing-sliding bifurcation", is observed, and the unfolding of the bifurcation is discussed. Based on the bifurcation analysis, five bursting oscillations associated with the codimension-2 bifurcation are observed, and the dynamical mechanism is revealed. The study suggests that the bifurcation of boundary equilibrium can be neither a non-smooth fold one nor a persistence one if the sliding vector field is degenerate, and this bifurcation may also lead to jumping behaviors in a bursting. A non-smooth limit cycle may cross the switching manifold transversely, precisely at the boundary of the escaping subregion, causing the limit cycle to disappear catastrophically. This bifurcation of non-smooth limit cycle controls the transition between a quiescent state and a spiking state in a bursting. A grazing-sliding bifurcation in a slow–fast system can form "reentry sliding structures" in a bursting. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09600779
- Volume :
- 184
- Database :
- Academic Search Index
- Journal :
- Chaos, Solitons & Fractals
- Publication Type :
- Periodical
- Accession number :
- 177854297
- Full Text :
- https://doi.org/10.1016/j.chaos.2024.115040