Introduction to the qualitative theory of differential systems : planar, symmetric and continuous piecewise linear systems
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Bibliographic Information
Introduction to the qualitative theory of differential systems : planar, symmetric and continuous piecewise linear systems
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhäuser : Springer, c2014
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Note
Includes bibliographical references (p. 283-286) and index
Description and Table of Contents
Description
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
Preface.- 1 Introduction and statement of the main results.- 2 Basic elements of the qualitative theory of ODEs.- 3 Fundamental systems.- 4 Return maps.- 5 Phase portraits.- Index.- Bibliography.
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