A generalized van der Pol type oscillator: Investigation of the properties of its limit cycle

A generalized van der Pol type oscillator is considered, with power-form nonlinearities in the restoring and damping force. The amplitude of the limit cycle is obtained by applying the generalized Krylov–Bogoliubov method for purely nonlinear oscillators. The influence of the values of the powers of the damping and the restoring force on this amplitude is investigated both analytically and numerically. The limiting values of this amplitude are found and the time for the amplitude to ‘nearly’ reach the limit cycle is estimated.