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

We have presented an unified scheme to express a class of system of equations in two variables into a Lienard–Levinson–Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Lienard 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.