Self-sustained Oscillations and Limit Cycles in Rayleigh System with Cubic Return Force

Abstract

An oscillatory system with an excitation mechanism as in a Rayleigh oscillator, but with a nonlinear (cubic) returning force, is investigated. Using the accelerated convergence method and the continuation procedure for the parameter, limit cycles are constructed and the amplitudes and periods of self-oscillations are calculated. This is done for a wide range of feedback coefficient values, in which this coefficient is not asymptotically small or large. The proposed iterative procedure allows to achieve the specified accuracy of calculations. The analysis of the features of the limit cycle caused by an increase in the self-excitation coefficient is carried out. The results obtained are compared with the self-oscillations of a classical Rayleigh oscillator with a linear returning force.