18-10 Alberto Strumia

An analytic approach to Van der Pol limit cycle (759K, pdf) Feb 3, 18

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Abstract. We propose a way to perform analytic integration of the Van der Pol unforced equation, in order to provide the Cartesian algebraic equation of the integral curve representing the Van der Pol limiting cycle. The method provides exact analytic solutions to the Van der Pol equation in the small control parameter (epsilon) approximation. A plot comparison with the results obtained with the numerical Runge-Kutta method is also examined. The present approach exhibits the advantage of dealing with the only geometry of the integral curve avoiding to involve kinematics, time dependence of the co-ordinate variable during motion.

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