Limit Cycle Article Index for
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Limit Cycle




Stable limit-cycles imply self sustained Oscillations . Any small perturbation from the closed trajectory would cause the system to return to the limit-cycle, making the system stick to the limit-cycle.

Figure illustrating a stable limit cycle for the Van Der Pol Oscillator . As seen in the figure, all the trajectories for various initial states of this system converge to the limit cycle. Hence, this system exhibits self-sustained oscillations.

Further Reading:
  • Steven H. Strogatz, "Nonlinear Dynamics and Chaos", Addison Wesley publishing company, 1994.


  • M. Vidyasagar, "Nonlinear Systems Analysis, second edition, Prentice Hall, Englewood Cliffs, New Jersey 07632.


and also:
  • Philip Hartman, "Ordinary Differential Equation", Society for Industrial and Applied Mathematics, 2002.


  • Witold Hurewicz, "Lectures on Ordinary Differential Equations", Dover, 2002.


  • Solomon Lefschetz, "Differential Equations: Geometric Theory", Dover, 2005.


  • Lawrence Perko, "Differential Equations and Dynamical Systems", Springer-Verlag, 2006.