Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles
arXiv:1904.00604 · doi:10.1007/s40819-019-0628-9
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.
9 Pages, Published online on 29/03/2019