Introduction to the Qualitative Theory of Differential Systems: Planar, Symmetric and Continuous Piecewise Linear Systems

✍ Scribed by Jaume Llibre, Antonio E. Teruel (auth.)

• Publisher: Springer Basel
• Year: 2014
• Tongue: English
• Leaves: 300
• Series: Birkhäuser Advanced Texts Basler Lehrbücher
• Edition: 1
• Category: Library

✦ Synopsis

The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, 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 infinity. The behavior of their solutions, their parametric stability or instability and their bifurcations are described. The book is very appropriate for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction and Statement of the Main Results....Pages 1-18
Basic Elements of the Qualitative Theory of Ordinary Differential Equations....Pages 19-59
Fundamental Systems....Pages 61-118
Return Maps....Pages 119-187
Phase Portraits....Pages 189-281
Back Matter....Pages 283-289

✦ Subjects

Ordinary Differential Equations; Systems Theory, Control; Partial Differential Equations