We analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small parameter at the highest derivative.
"Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control." Abstr. Appl. Anal. 2013 (SI28) 1 - 7, 2013. https://doi.org/10.1155/2013/848613