Generalization of hyperbolic perturbation solution for heteroclinic orbits of strongly nonlinear self-excited oscillator

Abstract

A generalized hyperbolic perturbation method for heteroclinic solutions is presented for strongly nonlinear self-excited oscillators in the more general form of $\stackrel{\mathrm{··}}{x}+g(x)=\varepsilon f(\mu ,x,\stackrel{·}{x})$ . The advantage of this work is that heteroclinic solutions for more complicated and strong nonlinearities can be analytically derived, and the previous hyperbolic perturbation solutions for Duffing type oscillator can be just regarded as a special case of the present method. The applications to cases with quadratic-cubic nonlinearities and with quintic-septic nonlinearities are presented. Comparisons with other methods are performed to assess the effectiveness of the present method.