Oscillatory Behavior in Linear Difference Equations under Unmodeled Dynamics and Parametrical Errors

De la Sen, M.

doi:https://doi.org/10.1155/2007/25692

Mathematical Problems in Engineering

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Research Article | Open Access

Volume 2007 | Article ID 025692 | https://doi.org/10.1155/2007/25692

Oscillatory Behavior in Linear Difference Equations under Unmodeled Dynamics and Parametrical Errors

M. De la Sen¹

Academic Editor: Jan Awrejcewicz

Received05 May 2006

Accepted22 Mar 2007

Published21 May 2007

Abstract

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.

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Copyright

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.

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