We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Global dynamics of a SD oscillator.
- Authors
Chen, Hebai; Llibre, Jaume; Tang, Yilei
- Abstract
In this paper, we derive the global bifurcation diagrams of a SD oscillator which exhibits both smooth and discontinuous dynamics depending on the value of a parameter <italic>a</italic>. We research all possible bifurcations of this system, including Pitchfork bifurcation, degenerate Hopf bifurcation, homoclinic bifurcation, double limit cycle bifurcation, Bautin bifurcation and Bogdanov–Takens bifurcation. Besides, we show that the system has five limit cycles, including four small limit cycles and one large limit cycle. At last, we give all numerical phase portraits to illustrate our results.
- Subjects
DYNAMICAL systems; BIFURCATION diagrams; HOPF bifurcations; LIMIT cycles; AVERAGING method (Differential equations)
- Publication
Nonlinear Dynamics, 2018, Vol 91, Issue 3, p1755
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-017-3979-y