On Stability of a Nonlinear Model with Delay
Author(s):
Alexander Vitalievich Prasolov
professor of Economic system modeling
doct. of science
Saint Petersburg State University
a.prasolov@spbu.ru
Leonid Stanislavovich Mikhlin
Master’s Degree in “Mathematical and information support in economic activity”
Saint Petersburg State University
mikhlin@bk.ru
Abstract:
In recent decades, a model in the form of a system of nonlinear
differential equations of the Lotka — Volterra type has been used
in dynamic problems of biology, economics, sociology, and others.
One of the important properties that characterizes the qualitative
behavior of such systems solutions is Lyapunov stability. This paper
is devoted to the analysis of the stability of the above mentioned systems
with a special type of delay. It is shown that in some cases it is possible
to calculate the critical delay at which the equilibrium solution loses stability.
Some generalizations of the Lotka — Volterra model are considered.
Examples from the field of economic dynamics illustrating the application of
the proposed method are given.
Keywords
- delay
- Lotka – Volterra system
- stability
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