Work

Periodic solutions in a linear delay difference system

Year: 2025

Type: article

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 apriori 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.

Source: Electronic journal of qualitative theory of differential equations

DOI: 10.14232/ejqtde.2025.1.10

Authors: Jan Čermák, Lucie Fedorková, Luděk Nechvátal

Institution: Brno University of Technology

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Vysoké Učení Technické v Brně

Award: G278839342