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Mathematical Problems in Engineering
Volume 2013, Article ID 650354, 8 pages
http://dx.doi.org/10.1155/2013/650354
Research Article

Active Control of Oscillation Patterns in the Presence of Multiarmed Pitchfork Structure of the Critical Manifold of Singularly Perturbed System

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

Received 2 September 2013; Revised 22 September 2013; Accepted 23 September 2013

Academic Editor: Hamid Reza Karimi

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.

Abstract

We analyze the possibility of control of oscillation patterns for nonlinear dynamical systems without the excitation of oscillatory inputs. We propose a general method for the partition of the space of initial states to the areas allowing active control of the stable steady-state oscillations. Furthermore, we show that the frequency of oscillations can be controlled by an appropriately positioned parameter in the mathematical model. This paper extends the knowledge of the nature of the oscillations with emphasis on its consequences for active control. The results of the analysis are numerically verified and provide the feedback for further design of oscillator circuits.