MATHEMATICS

On constructing a stability region for a linear discrete-time autonomous equation of the fourth order

V. A. Zaitsev, A. S. Bannikov, P. S. Khalyavina

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: For an autonomous fourth-order linear difference equation, the stability domain $S_4$ in four-dimensional space is investigated, the parameters of which are the equation coefficients. Sections of the domain $S_4$ by hyperplanes of four-dimensional space are studied and constructed in three-dimensional space for a fixed value of the fourth parameter. It is shown that these sections are diffeomorphic to the stability domain $S_3$ of the third-order linear difference equation.

Keywords: linear difference equation, Schur stability, stability region

UDC: 517.925.51

MSC: 39A06, 39A30

Received: 03.07.2025
Accepted: 11.10.2025

Language: English

DOI: 10.35634/vm250402

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