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Mathematics - Dynamical Systems & Differential Equations | Introduction to the Qualitative Theory of Differential Systems - Planar, Symmetric and Continuous

Introduction to the Qualitative Theory of Differential Systems

Planar, Symmetric and Continuous Piecewise Linear Systems

Llibre, Jaume, Teruel, Antonio E.

2014, XIII, 289 p. 84 illus., 1 illus. in color.

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  • 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
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.

Content Level » Graduate

Keywords » Poincaré map - bifurcation, bifurcation diagram - compactification - periodic solutions - qualitative theory

Related subjects » Applications - Dynamical Systems & Differential Equations

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