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Volume 12   Issue 2   Year 2017
On The Correlation between Properties of One-Dimensional Mappings of Control Functions and Chaos in a Special Type Delay Differential Equation

Vitaliy A. Likhoshvai, Vladislav V. Kogai, Stanislav I. Fadeev, Tamara M. Khlebodarova

Federal Research Center Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Novosibirsk National Research State University, 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  /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  /g.
Key words: modeling, deterministic chaos, equations with delayed argument, feedback regulation.


Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2017.12.385
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)


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