Piecewise Bounded Quadratic Systems in the Plane

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• 作者：Jaume Llibre ; Clayton E. L. da Silva…
• 关键词：Non ; smooth dynamical systems ; Quadratic systems ; Bounded quadratic systems ; Sliding vector fields ; Phase portrait ; 34C15 ; 34K12 ; 34H05
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：24
• 期：1
• 页码：51-62
• 全文大小：728 KB
• 参考文献：1.Coll, B., Gasull, A., Llibre, J.: Some theorems on the existence, uniqueness, and nonexistence of limit cycles for quadratic systems. J. Differ Equ. 67, 372–399 (1987)CrossRef MathSciNet MATH
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  3.Dickson, R., Perko, L.: Bounded quadratic systems in the plane. J. Differ. Equ. 7, 251–273 (1970)CrossRef MathSciNet MATH
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  6.Markus, L.: Quadratic differential equations and non-associative algebras. Ann. Math. Stud. 45, 185–213. Princeton University Press, Princeton (1960)
  
• 作者单位：Jaume Llibre (1)
  Clayton E. L. da Silva (2)
  Paulo R. da Silva (2)
  
  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain
  2. Deparatamento de Matemática, Instituto de Biociências Letras e Ciências Exatas, UNESP - Univ Estadual Paulista, São José do Rio Preto, São Paulo, Brazil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  
• 出版者：Springer India
• ISSN：0974-6870

文摘

In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field \(Z=(X,Y)\). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded. Keywords Non-smooth dynamical systems Quadratic systems Bounded quadratic systems Sliding vector fields Phase portrait