Introduction to the Qualitative Theory of Differential Systems

This book introduces the basic tools of the qualitative theory of ordinary differential equations. It is ideal for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.

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.

Excellent for learning the use of basic results on qualitative theory of differential systems Illustrates how to use the Poincaré map for studying the periodic orbits of a differential system Shows the importance of compactification of the domain of definition of a differential system for the understanding of the global dynamics of the system Points out the importance of bifurcation diagrams for describing the different dynamics of differential systems depending on parameters Includes supplementary material: sn.pub/extras

Auteur
Jaume Llibre is full professor at the Autonomous University of Barcelona (Spain) and a member of the Royal Academy of Sciences and Arts of Barcelona. He was a long-term visitor at different important universities and research institutes and is the author of many papers and some books. His main results deal with the periodic orbits either of different kinds of self-maps, or of vector fields, Hamiltonian systems and celestial mechanics. Antonio E. Teruel is associated professor at the University of the Balear Islands (Spain). He is the author of some papers about piecewise linear differential systems. His main results deal with piecewise linear models of differential behaviors.

Contenu
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.