Analytical and Numerical Studies of Periodic Solutions Outside Potential Wells

Analytical and numerical methods of nonlinear dynamics are used to study the existence of the periodic solutions outside potential wells which were not studied in our previous works. We obtain analytically the conditions for which the periodic solutions of the strongly non-linear perturbed oscillators of the form X+AX-(pBX''p-1)/2) + epsilon f (X,X')=0 exist. These oscillators are dissipative models for which periodic solutions are known to exist for limited ranges of the parameter values and initial conditions. These conditions are tested numerically and good agreement is found. We find that these periodic solutions have finite periods and to every limit cycle inside these potential wells there exists a periodic solution outside them. (Author) 11 refs