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arXiv · 1904.00604

Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles

Sandip Saha·Gautam Gangopadhyay·Deb Shankar Ray
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Abstract

We have presented an unified scheme to express a class of system of equations in two variables into a Liénard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Liénard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases.

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Sandip Saha, Gautam Gangopadhyay, Deb Shankar Ray. 2019-04-02. Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles. https://doi.org/10.1007/s40819-019-0628-9

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