Analysis of oscillations in quasi-conservative strongly nonlinear oscillator systems

The oscillations in a perturbed Duffing oscillator have been analyzed. The oscillations are regarded as limit cycles in a perturbed Hamiltonian system under polynomial perturbation of the sixth degree and analyzed by using the Melnikov function. It has been proved that there exists a polynomial perturbation depending on the zeros of the Melnikov function so that the system considered can have either two simple limit cycles, or one limit cycle of multiplicity 2, or one simple limit cycle.