A hyperbolic Lindstedt-Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators. (English) Zbl 1269.70031

Summary: A hyperbolic Lindstedt-Poincaré method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Liénard oscillator is studied in detail, and the present method’s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.


70K44 Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics
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