Introduction to the Qualitative Theory of Differential Systems [electronic resource] : Planar, Symmetric and Continuous Piecewise Linear Systems / by Jaume Llibre, Antonio E. Teruel.
By: Llibre, Jaume [author.].
Contributor(s): Teruel, Antonio E [author.] | SpringerLink (Online service).
Material type:
BookSeries: Birkhäuser Advanced Texts Basler Lehrbücher: Publisher: Basel : Springer Basel : Imprint: Springer, 2014Description: XIII, 289 p. 84 illus., 1 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783034806572.Subject(s): Mathematics | Differential Equations | Differential equations, partial | Systems theory | Mathematics | Ordinary Differential Equations | Systems Theory, Control | Partial Differential EquationsDDC classification: 515.352 Online resources: Click here to access online 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. .
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.
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