Piecewise Bounded Quadratic Systems in the Plane

Jaume Llibre, Clayton E.L. da Silva, Paulo R. da Silva

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


© 2014, Foundation for Scientific Research and Technological Innovation. In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field $$Z=(X,Y)$$Z=(X,Y). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.
Original languageEnglish
Pages (from-to)51-62
JournalDifferential Equations and Dynamical Systems
Issue number1
Publication statusPublished - 1 Jan 2016


  • Bounded quadratic systems
  • Non-smooth dynamical systems
  • Phase portrait
  • Quadratic systems
  • Sliding vector fields


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