Harmonic balance approach to limit cycles for nonlinear jerk equations

Abstract

The method of harmonic balance (HB) is employed to estimate the attributes of limit cycles of some nonlinear third-order (jerk) differential equations which are parity-invariant but not time-reversal-invariant. Two examples with cubic nonlinearities show that the HB method can give good values for the frequency and both the velocity and displacement amplitudes of a period one limit cycle.