Introduction to the Qualitative Theory of Differential Systems

Planar, Symmetric and Continuous Piecewise Linear Systems

  • Jaume Llibre
  • Antonio E. Teruel

Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jaume Llibre, Antonio E. Teruel
    Pages 1-18
  3. Jaume Llibre, Antonio E. Teruel
    Pages 61-118
  4. Jaume Llibre, Antonio E. Teruel
    Pages 119-187
  5. Jaume Llibre, Antonio E. Teruel
    Pages 189-281
  6. Back Matter
    Pages 283-289

About this book


The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. These differential systems are symmetric with respect to the origin of coordinates. This class of systems, driven by concrete applications, is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems, we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these systems including the dynamics at infinity. The behavior of their solutions, their parametric stability or instability and their bifurcations are described. The book is highly suitable for a first course in the qualitative theory of differential equations or dynamical systems, particularly for engineers, mathematicians, and physicists.


Poincaré map bifurcation, bifurcation diagram compactification periodic solutions qualitative theory

Authors and affiliations

  • Jaume Llibre
    • 1
  • Antonio E. Teruel
    • 2
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Dept. de Matemàtiques i InformàticaUniversitat de les Illes BalearsPalma-Illes BalearsSpain

Bibliographic information