Advertisement

Layer Analysis

  • Mike R. Jeffrey
Chapter

Abstract

In this section we discuss dynamics inside the switching layer , looking at how to apply fundamental notions like stability analysis and linearization across a discontinuity.

References

  1. 30.
    J. Carr. Applications of center manifold theory. Springer-Verlag, 1981.Google Scholar
  2. 48.
    M. di Bernardo, C. J. Budd, A. R. Champneys, and P. Kowalczyk. Piecewise-Smooth Dynamical Systems: Theory and Applications. Springer, 2008.Google Scholar
  3. 52.
    L. Dieci, C. Elia, and L. Lopez. A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis. J. Differential Equations, 254:1800–1832, 2013.MathSciNetzbMATHGoogle Scholar
  4. 53.
    L. Dieci and L. Lopez. Sliding motion on discontinuity surfaces of high co-dimension. a construction for selecting a Filippov vector field. Numer. Math., 117:779–811, 2011.Google Scholar
  5. 68.
    N. Fenichel. Geometric singular perturbation theory. J. Differ. Equ., 31:53–98, 1979.MathSciNetzbMATHGoogle Scholar
  6. 71.
    A. F. Filippov. Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publ. Dortrecht, 1988 (Russian 1985).Google Scholar
  7. 92.
    J. Guckenheimer and P. Holmes. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Applied Mathematical Sciences 42. Springer, 2002.Google Scholar
  8. 98.
    P. Hartman. Ordinary differential equations. Wiley: New York, 1964.zbMATHGoogle Scholar
  9. 113.
    M. R. Jeffrey. Dynamics at a switching intersection: hierarchy, isonomy, and multiple-sliding. SIADS, 13(3):1082–1105, 2014.MathSciNetzbMATHGoogle Scholar
  10. 124.
    C. K. R. T. Jones. Geometric singular perturbation theory, volume 1609 of Lecture Notes in Math. pp. 44–120. Springer-Verlag (New York), 1995.Google Scholar
  11. 126.
    A. Kelley. The stable, center stable, center, center unstable and unstable manifolds. J. Diff. Eqns., 3:546–570, 1967.MathSciNetzbMATHGoogle Scholar
  12. 135.
    C. Kuehn. Multiple time scale dynamics. Springer, 2015.Google Scholar
  13. 138.
    Y. A. Kuznetsov. Elements of Applied Bifurcation Theory. Springer, 3rd Ed., 2004.Google Scholar
  14. 161.
    J. E. Marsden and M. McCracken. The Hopf bifurcation and its applications. Springer-Verlag, 1976.Google Scholar
  15. 187.
    J. Sijbrand. Studies in nonlinear stability and bifurcation theory. Rijksuniversiet Utrecht, 1981.Google Scholar
  16. 211.
    V. I. Utkin. Variable structure systems with sliding modes. IEEE Trans. Automat. Contr., 22:212–222, 1977.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mike R. Jeffrey
    • 1
  1. 1.Department of Engineering MathematicsUniversity of BristolBristolUK

Personalised recommendations