Piecewise Bounded Quadratic Systems in the Plane

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

doi:https://doi.org/10.1007/s12591-014-0205-y

Piecewise Bounded Quadratic Systems in the Plane

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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 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 language	English
Pages (from-to)	51-62
Journal	Differential Equations and Dynamical Systems
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s12591-014-0205-y
Publication status	Published - 1 Jan 2016

Keywords

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

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https://doi.org/10.1007/s12591-014-0205-y

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title = "Piecewise Bounded Quadratic Systems in the Plane",

abstract = "{\textcopyright} 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.",

keywords = "Bounded quadratic systems, Non-smooth dynamical systems, Phase portrait, Quadratic systems, Sliding vector fields",

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N2 - © 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.

AB - © 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.

KW - Bounded quadratic systems

KW - Non-smooth dynamical systems

KW - Phase portrait

KW - Quadratic systems

KW - Sliding vector fields

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