Mathematics

On a hidden attractor of one asymmetric gene network model

V. P. Golubyatnikov, Sitnyakovskaya Elizaveta A

Novosibirsk State University

Abstract: We consider a model of simplest circular gene network regulated by one negative and two positive feedbacks. The model is represented in the form of 3-dimensional dynamical system with piecewise linear threshold righthand sides. In the phase portrait of this system, we describe a hidden attractor. Conditions of existence and uniqueness of a cycle of this system are established.

Keywords: phase portrait of dynamical system, equilibrium point, stratification of the phase portrait, invariant domain, multi-step function, cycle, non-local oscillation, hidden attractor

UDC: 517.938

Received: 20.03.2024
Accepted: 30.05.2024

DOI: 10.25587/2411-9326-2024-2-3-13