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JOURNALS // Matematicheskaya Biologiya i Bioinformatika // Archive

Mat. Biolog. Bioinform., 2017 Volume 12, Issue 2, Pages 385–397 (Mi mbb301)

This article is cited in 3 papers

Mathematical Modeling

On the correlation between properties of one-dimensional mappings of control functions and chaos in a special type delay differential equation

V. A. Likhoshvaiab, V. V. Kogaica, S. I. Fadeevca, T. M. Khlebodarovab

a Novosibirsk National Research State University, Novosibirsk, Russia
b Federal Research Center Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: A differential equation of a special form, which contains two control functions $f$ and $g$ and one delayed argument, is analyzed. This equation has a wide application in biology for the description of dynamic processes in population, physiological, metabolic, molecular-genetic, and other applications. Specific numerical examples show the correlation between the properties of the one-dimensional mapping, which is generated by the ratio $f /g$, and the presence of chaotic dynamics for such equation. An empirical criterion is formulated that allows one to predict the presence of a chaotic potential for a given equation by the properties of the one-dimensional mapping $f /g$.

Key words: modeling, deterministic chaos, equations with delayed argument, feedback regulation.

UDC: 530.182.2:573.7

Received 25.09.2017, Published 07.11.2017

DOI: 10.17537/2017.12.385



© Steklov Math. Inst. of RAS, 2025