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Introductory Notes on the Dynamics of Linear and Linearized Systems

  • Marji Lines
  • Alfredo Medio
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 476)

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.*

Keywords

Equilibrium Point Jacobian Matrix Hopf Bifurcation Unstable Manifold Centre Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Marji Lines
    • 1
  • Alfredo Medio
    • 1
  1. 1.Department of StatisticsUniversity of UdineUdineItaly

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