Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 848613, 7 pages
Research Article

Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control

Faculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdoczyho 1, 917 01 Trnava, Slovakia

Received 21 June 2013; Revised 9 August 2013; Accepted 21 August 2013

Academic Editor: Elena Braverman

Copyright © 2013 Robert Vrabel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.