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

• Κύριοι συγγραφείς: Llibre, Jaume (Συγγραφέας), Teruel, Antonio E. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Springer Basel : Imprint: Springer, 2014.
• Σειρά: Birkhäuser Advanced Texts Basler Lehrbücher,
• Θέματα: Mathematics.; Differential equations.; Partial differential equations.; System theory.; Ordinary Differential Equations.; Systems Theory, Control.; Partial Differential Equations.

 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. 

 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.  .