Canonical Discontinuous Planar Piecewise Linear Systems

@article{Freire2012CanonicalDP,
  title={Canonical Discontinuous Planar Piecewise Linear Systems},
  author={Emilio Freire and Enrique Ponce and Francisco Torres},
  journal={SIAM J. Applied Dynamical Systems},
  year={2012},
  volume={11},
  pages={181-211}
}
The family of Filippov systems constituted by planar discontinuous piecewise linear systems with two half-plane linearity zones is considered. Under generic conditions that amount to the boundedness of the sliding set, some changes of variables and parameters are used to obtain a Liénard-like canonical form with seven parameters. This canonical form is topologically equivalent to the original system if one restricts one’s attention to orbits with no points in the sliding set. Under the… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 18 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 24 references

Differential Equations with Discontinuous Right-Hand Sides, Kluwer Academic Publishers, Dordrecht

  • A. F. Filippov
  • The Netherlands,
  • 1988
Highly Influential
15 Excerpts

On the number of limit cycles in general planar piecewise linear systems

  • S. Huan, X. Yang
  • Discrete Contin. Dynam. Systems,
  • 2012
Highly Influential
5 Excerpts

On Hopf bifurcation in non-smooth planar systems

  • M. Han, W. Zhang
  • J. Differential Equations,
  • 2010
1 Excerpt

The qualitative analysis of a class of planar Filippov systems

  • S. Shui, X. Zhang, J. Li
  • Nonlinear Anal.,
  • 2010
1 Excerpt

The qualitative analysis of a class of planar Filippov systems , Nonlinear Anal

  • X. Zhang, J. Li
  • 2010

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

  • E. Ponce J. Llibre, F. Torres
  • Nonlinearity
  • 2008

Similar Papers

Loading similar papers…