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This article is cited in 3 scientific papers (total 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.
Received 25.09.2017, Published 07.11.2017
Citation:
V. A. Likhoshvai, V. V. Kogai, S. I. Fadeev, T. M. Khlebodarova, “On the correlation between properties of one-dimensional mappings of control functions and chaos in a special type delay differential equation”, Mat. Biolog. Bioinform., 12:2 (2017), 385–397
Linking options:
https://www.mathnet.ru/eng/mbb301 https://www.mathnet.ru/eng/mbb/v12/i2/p385
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Abstract page: | 184 | Full-text PDF : | 99 | References: | 26 |
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