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.
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
\Bibitem{LikKogFad17}
\by V.~A.~Likhoshvai, V.~V.~Kogai, S.~I.~Fadeev, T.~M.~Khlebodarova
\paper On the correlation between properties of one-dimensional mappings of control functions and chaos in a special type delay differential equation
\jour Mat. Biolog. Bioinform.
\yr 2017
\vol 12
\issue 2
\pages 385--397
\mathnet{http://mi.mathnet.ru/mbb301}
\crossref{https://doi.org/10.17537/2017.12.385}
Linking options:
https://www.mathnet.ru/eng/mbb301
https://www.mathnet.ru/eng/mbb/v12/i2/p385
This publication is cited in the following 3 articles:
Khlebodarova T.M. Kogai V.V. Likhoshvai V.A., “On the Dynamical Aspects of Local Translation At the Activated Synapse”, BMC Bioinformatics, 21:11, SI (2020), 258
V. A. Likhoshvai, T. M. Khlebodarova, “On stationary solutions of delay differential equations: a model of local translation in synapses”, Mat. Biolog. Bioinform., 14:2 (2019), 554–569
T. M. Khlebodarova, V. V. Kogai, E. A. Trifonova, V. A. Likhoshvai, “Dynamic landscape of the local translation at activated synapses”, Mol. Psychiatr., 23:1 (2018), 107–114
Citation in format AMSBIB
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