Bifurcation of Periodic Solutions of the Mackey– Glass Equation
https://doi.org/10.18255/1818-1015-2016-6-784-803
Abstract
We study the bifurcation of the equilibrium states of periodic solutions for the Mackey– Glass equation. This equation is considered as a mathematical model of changes in the density of white blood cells. The equation written in dimensionless variables contains a small parameter at the derivative, which makes it singular. We applied the method of uniform normalization, which allows us to reduce the study of the solutions behavior in the neighborhood of the equilibrium state to the analysis of the countable system of ordinary differential equations. We poot out the equations in ”fast” and ”slow” variables from this system. Equilibrium states of the ”slow” variables equations determine the periodic solutions. The analysis of equilibrium states allows us to study the bifurcation of periodic solutions depending on the parameters of the equation and their stability. The possibility of simultaneous bifurcation of a large number of stable periodic solutions is shown. This situation is called the multistability phenomenon.
About the Authors
E. P. Kubyshkin
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
Doctor, Professor, 14 Sovetskaya str., Yaroslavl 150003, Russia
A. R. Moryakova
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
graduate student, 14 Sovetskaya str., Yaroslavl 150003, Russia
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Review
For citations:
Kubyshkin E.P., Moryakova A.R. Bifurcation of Periodic Solutions of the Mackey– Glass Equation. Modeling and Analysis of Information Systems. 2016;23(6):784-803. (In Russ.) https://doi.org/10.18255/1818-1015-2016-6-784-803
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