Dynamics of Discontinuous Systems with Imperfections and Noise

  • Tom Griffin
  • S. John Hogan
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 122)


Many physical systems of engineering importance are discontinuous (examples include systems with impacts, freeplay, backlash, gears). The study of deterministic versions of these systems is now well established but these models tend to ignore any imperfections in the system or the effects of noise. In this paper we show how the introduction of imperfections and noise can have a dramatic effect on the systems behaviour. We focus our attention on a much studied simple generic model of discontinuous systems, namely that of the piecewise linear map and its associated ordinary differential equation.

Key words

Discontinuous systems imperfections noise 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M.I. Feigin, “Fundamental dynamic models and criteria of C-bifurcation structures for piecewise smooth systems,” Proceedings of the International Symposium on Analysis and Synthesis of Nonlinear Dynamical Systems, 30–40, June, Riga, Latvia, 1996.Google Scholar
  2. [2]
    M. Di Bernardo, M. Feigin, S. Hogan and M. Homer, “Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems,” Chaos Solitons and Fractals, Vol. 10, No. 11, pp. 1881–1908, 1999.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Tom Griffin
    • 1
  • S. John Hogan
    • 1
  1. 1.Applied Nonlinear Mathematics GroupUniversity of BristolEngland

Personalised recommendations