Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 25692, 18 pages
Oscillatory Behavior in Linear Difference Equations under Unmodeled Dynamics and Parametrical Errors
Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, Campus of Leioa, Bizkaia, Aptdo, Bilbao 544, Spain
Received 5 May 2006; Accepted 22 March 2007
Academic Editor: Jan Awrejcewicz
Copyright © 2007 M. De la Sen. 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.
This paper investigates the presence of oscillating solutions in time-varying
difference equations even in the case when there exist parametrical errors
(i.e., errors in the sequences defining their coefficients) and/or unmodeled dynamics,
namely, the current order is unknown and greater than the nominal known
order. The formulation is related to the concepts of conjugacy, disconjugacy,
positivity, and generalized zeros and general conditions of oscillation are obtained
both over particular intervals and for the whole solution. Some results concerned with
the presence of stable oscillations are also presented.