Mathematics

On stability of cycles in some piecewise dynamical systems of mathematical biology

A. V. Glubokikh^a, V. P. Golubyatnikov^b, E. P. Volokitin<sup>b

a</sup> Novosibirsk State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: For a piecewise linear three-dimensional dynamical system of biochemical kinetics with three-steps righthand sides, we find conditions of existence of two stable cycles in the phase portrait. Toroidal neighborhoods of these cycles are constructed.

Keywords: mathematical modelling, piecewise-linear dynamical systems, phase portrait, cycle, stability, the Poincar´e map

UDC: 517.938

Received: 29.12.2024
Accepted: 25.02.2025

DOI: 10.25587/2411-9326-2025-1-4-14