High Accurate Homo-Heteroclinic Solutions of Certain Strongly Nonlinear Oscillators Based on Generalized Pade-Lindstedt-Poincare Method

Background In this work, the generalized Pade-Lindstedt-Poincare method is applied to obtain high accurate homoclinic and heteroclinic solutions of the entire Phi(6)-Van der Pol oscillator with asymmetric potential and the generalized Duffing-Harmonic-Van der Pol oscillator. Meanwhile, the critical values of bifurcation parameter are also predicted Methods To improve the efficiency and accuracy, several new types of generalized Pade approximant are constructed and introduced into the procedure of the present method. In this method, the perturbation equations obtained from the Lindstedt-Poincare procedures are solved by generalized Pade approximation method instead of the traditional integration method. Consequently, the proposed method does not involve the cumbersome calculations of derivation and integration compared to traditional perturbation-based methods. It means that the high order perturbation solutions can be easily obtained via the present method. Results To demonstrate the feasibility of the method, the oscillators with small and big parameters are both solved. All solutions and critical values obtained in this paper are compared to the results obtained from the Runge-Kutta method. It shows high agreement between the present results and the numerical ones. Conclusion In general, this method has characters of simple calculation, high accuracy and wide applicability, which can be regarded as a supplement and improvement of existing perturbation-based method.