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Sliding Vector Fields via Slow-Fast Systems
(Belgian Mathematical Soc Triomphe, 2008-01-01)
This paper concerns differential equation systems on R(n) with discontinuous right-hand sides. We deal with non-smooth vector fields in R(n) having a codimension-one submanifold M as its discontinuity set. After a ...
Sliding vector fields via slow-fast systems
(2008-01-01)
This paper concerns differential equation systems on ℝn with discontinuous right-hand sides. We deal with non-smooth vector fields in ℝ having a codimension-one submanifold M as its discontinuity set. After a regularization ...
Nonlinear Sliding of Discontinuous Vector Fields and Singular Perturbation
(2020-01-01)
We consider piecewise smooth vector fields (PSVF) defined in open sets M⊆ Rn with switching manifold being a smooth surface Σ. We assume that M\ Σ contains exactly two connected regions, namely Σ + and Σ -. Then, the PSVF ...
Peixoto's Theorem for vector fields on S2 with impasse points
(2013-09-01)
The structural stability of vector fields with impasse regular curves on S2 is studied and a version of Peixoto's Theorem is established. Moreover a global analysis of normal forms of the constrained systems. A(x).ẋ=F(x) ...
Sliding Vector Fields via Slow-Fast Systems
(Belgian Mathematical Soc TriompheBrusselsBélgica, 2008)
Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
(2017-05-15)
In this paper, Hopf and homoclinic bifurcations that occur in the sliding vector field of switching systems in R3 are studied. In particular, a dc–dc boost converter with sliding mode control and washout filter is analyzed. ...
Synchronization and Non-Smooth Dynamical Systems
(Springer, 2012-03-01)
In this article we establish an interaction between non-smooth systems, geometric singular perturbation theory and synchronization phenomena. We find conditions for a non-smooth vector fields be locally synchronized. ...
Regularization and singular perturbation techniques for non-smooth systems
(Elsevier B.V., 2012-11-15)
This paper is concerned with some aspects of the qualitative-geometric theory of non-smooth systems. We present a survey of the state of the art on the connection between the regularization process of nonsmooth vector ...
Codimension two singularities of sliding vector fields
(Societe Mathematique BelgiqueBrusselsBélgica, 1999)
Regularization and singular perturbation techniques for non-smooth systems
(Elsevier Science BvAmsterdamHolanda, 2012)