• To introduce bifurcation theory in the plane.

  • To introduce the notion of steady-state solution and investigate multistability and bistability.


Vector Field Saddle Point Hopf Bifurcation Phase Portrait Bifurcation Diagram 
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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Recommended Reading

  1. 1.
    K. Ikeda and K. Murota, Imperfect Bifurcations in Structures and Materials, Springer-Verlag, New York, 2002.CrossRefGoogle Scholar
  2. 2.
    J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos, 2nd ed., Wiley, New York, 2002.MATHGoogle Scholar
  3. 3.
    S. H. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering, Perseus Books, New York, 2001.Google Scholar
  4. 4.
    M. Demazure and D. Chillingworth (translator), Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems, Springer-Verlag, New York, 2000.Google Scholar
  5. 5.
    S. Lynch and C. J. Christopher, Limit cycles in highly nonlinear differential equations, J. Sound Vibration, 224-3 (1999), 505-517.MathSciNetCrossRefGoogle Scholar
  6. 6.
    G Iooss and D. D. Joseph, Elementary Stability and Bifurcation Theory, Springer-Verlag, New York, 1997.Google Scholar
  7. 7.
    R. Seydel, Practical Bifurcation and Stability Analysis, from Equilibrium to Chaos, Springer-Verlag, New York, 1994.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Stephen Lynch
    • 1
  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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