A novel construction of homoclinic and heteroclinic orbits in nonlinear oscillators by a perturbation-incremental method

A novel construction of homoclinic/heteroclinic orbits (HOs) in nonlinear oscillators is presented in this paper. An accurate analytical solution of a HO for small perturbation can be obtained in terms of trigonometric functions. An advantage of the present construction is that it gives an accurate approximate solution of a HO for large parametric value in relatively few harmonic terms while other analytical methods such as the Lindstedt–Poincaré method and the multiple scales method fail to do so.

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