Introductory Notes on the Dynamics of Linear and Linearized Systems

Abstract

In the following we provide terminology and concepts which are central to understanding the dynamical behavior of nonlinear systems. The first four sections are a necessarily very brief introduction to the dynamics of linear systems, in which we concentrate on those aspects most useful for acquiring a sense of the basic behaviours characterising systems of differential and difference equations. The last four sections introduce basic notions of stability, the linear approximation and the Hartman-Grobman Theorem, the use of the Centre Manifold Theorem, local bifurcation theory.*

For suggestions on further reading and an extended bibliography please see Medio and Lines, Nonlinear Dynamics: A Primer, Cambridge: Cambridge University Press, 2001.