Periodic solutions in a linear delay difference system
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Date
2025-04-05
Authors
Čermák, Jan
Fedorková, Lucie
Nechvátal, Luděk
0000-0002-6884-917XAdvisor
Referee
Mark
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Volume Title
Publisher
Bolyai Institute, University of Szeged
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Abstract
The paper investigates periodicity properties of a linear autonomous difference system with two delayed terms. Assuming that the system matrices are simultaneously triangularizable, we formulate necessary and sufficient conditions guaranteeing the existence of a nonzero periodic solution (with an a priori given period) of the studied system. The analytical form of such conditions is shown to generalize the existing results on this topic. Moreover, it is supported by a geometric reformulation, offering a better understanding of the derived periodicity conditions. Information on the form of the searched periodic solution (including its prime period) is also provided.
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Electronic Journal of Qualitative Theory of Differential Equations. 2025, vol. 2025, issue 10, p. 1-18.
https://www.math.u-szeged.hu/ejqtde/p11513.pdf
https://www.math.u-szeged.hu/ejqtde/p11513.pdf
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Peer-reviewed
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en