On the stability of nonlocal oscillations in one piecewise-linear dynamical system

A. V. Glubokikh

Novosibirsk State University, Novosibirsk, Russia

Abstract: We study the structure of the phase portrait of a three-dimensional dynamical system simulating the functioning of a simple molecular repressilator. The existence of a unique asymptotically stable equilibrium point is proven. Conditions for the existence and stability of a closed trajectory lying in the complement to the domain of attraction of this point are obtained.

Key words: gene network models, dynamical systems, phase portraits, equilibrium points, periodic solutions, step functions, nonlocal oscillations.

UDC: 517.938

Received: 14.09.2024
Revised: 22.12.2024
Accepted: 29.01.2025

DOI: 10.25205/1560-750X-2025-28-1-5-15