Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

الملخص EN

The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure.

The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method.

The application of the present homoclinic solutions to the chaos prediction of the nonautonomous Helmholtz-Duffing oscillator is performed.

Effectiveness and advantage of the present solutions are shown by comparisons.