Melnikov's method for a general nonlinear vibro-impact oscillator
The classical Melnikov's method is applied to a second order differential equation with impact effects. The equation is a perturbation of a Hamiltonian system with a homoclinic orbit to the origin. Then the first-order Melnikov function can be obtained analytically in the usual way. The method is applied to a double-well Duffing oscillator with impacts, thus obtaining a chaotic threshold, and complemented with some numerical computations.
scientific article; zbMATH DE number 5563045