ON THE SLIDING BIFURCATION OF A CLASS OF PLANAR FILIPPOV SYSTEMS

DOI10.1142/S0218127413500405zbMath1270.34088MaRDI QIDQ2845164

Xiang Zhang, Dingheng Pi, Jiang Yu

Publication date: 22 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

heteroclinic cyclepiecewise smooth differential systemssliding homoclinic bifurcationsemistable limit cycle bifurcationsliding-crossing bifurcation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Ordinary differential inclusions (34A60) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (11)

Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth systems with a cusp ⋮ The center problem on piecewise smooth differential systems with two zones ⋮ Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems ⋮ The sliding bifurcations in planar piecewise smooth differential systems ⋮ Periodic orbits for planar piecewise smooth systems with a line of discontinuity ⋮ Averaging theory of arbitrary order for piecewise smooth differential systems and its application ⋮ On typical homoclinic-like loops in 3D Filippov systems ⋮ Non-smooth ecological systems with a switching threshold depending on the pest density and its rate of change ⋮ Bifurcations of a generalized heteroclinic loop in a planar piecewise smooth system with periodic perturbations ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems

Cites Work

• Generic bifurcations of low codimension of planar Filippov systems
• An example of chaotic behaviour in presence of a sliding homoclinic orbit
• A singular approach to discontinuous vector fields on the plane
• Bifurcation and chaos near sliding homoclinics
• On Hopf bifurcation in non-smooth planar systems
• Quadratic Hamiltonian vector fields
• Qualitative bifurcation analysis of a non-smooth friction-oscillator model
• Two-parameter degenerate sliding bifurcations in Filippov systems
• Planar systems of piecewise linear differential equations with a line of discontinuity
• On the Regularization of Sliding Modes
• On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
• Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach
• Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation
• HOPF BIFURCATION FOR NONSMOOTH LIÉNARD SYSTEMS
• One-Parameter Bifurcations in Planar Filippov Systems
• Canonical Discontinuous Planar Piecewise Linear Systems
• Sliding mode observers: a survey

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