Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by the hyperbolic perturbation method

摘要

The hyperbolic perturbation method is applied to determining the homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators of the form [(x)ddot]+c₁x+c₃x3=ef(m,x,[(x)dot])ddot{x}+c_{1}x+c_{3}x^{3}=varepsilon f(mu,x,dot{x}) , in which the hyperbolic functions are employed instead of the periodic functions in the usual perturbation method. The generalized Liénard oscillator with f(m,x,[(x)dot])=(m-m₁x2-m₂[(x)dot]2)[(x)dot]f(mu,x,dot{x})=(mu -mu_{1}x^{2}-mu_{2}dot{x}^{2})dot{x} is studied in detail. Comparisons with the numerical simulations obtained by using R–K method are made to show the efficacy and accuracy of the present method.