• To give a brief historical background.

  • To define features of phase plane portraits.

  • To introduce the theory of planar limit cycles.


Phase Portrait Jordan Curve Nearby Trajectory Wing Rock Phase Plane Portrait 


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Recommended Reading

  1. 1.
    L. Perko, Differential Equations and Dynamical Systems, 3 rd ed., Springer-Verlag, New York, 2001.Google Scholar
  2. 2.
    J. A. Yorke (contributor), K. Alligood (ed.), and T. Sauer (ed.), Chaos: An Introduction to Dynamical Systems, Springer-Verlag, New York, 1996.Google Scholar
  3. 3.
    Ye Yon Qian, Theory of Limit Cycles, Translations of Mathematical Monographs 66, American Mathematical Society, Providence, 1986.Google Scholar
  4. 4.
    J. Rayleigh, The Theory of Sound, Dover, New York, 1945.Google Scholar
  5. 5.
    A. Liénard, Étude des oscillations entrenues, Rev. Gén. Électricité, 23 (1928), 946–954.Google Scholar
  6. 6.
    B. van der Pol, On relaxation oscillations, Philos. Magazine, 7 (1926), 901912, 946–954.Google 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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