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Model. Anal. Inform. Sist., 2017, Volume 24, Number 3, Pages 365–386 (Mi mais571)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical model of Nicholson's experiment

S. D. Glyzinab

a Scientific Center in Chernogolovka RAS, 9 Lesnaya str., Chernogolovka, Moscow region, 142432, Russia
b P.G. Demidov Yaroslavl State University, 14 Sovetskaya str., Yaroslavl 150003, Russia

Abstract: Considered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson's experiment is described and dynamic equations for its modeling are chosen. A priori estimates for model parameters can be made more precise by means of local analysis of the dynamical system, that is carried out in the second section. For parameter values found there the stability loss of the problem equilibrium of the leads to the bifurcation of a stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain the classical Nicholson's experiment, whose detailed theoretical substantiation is given in the last section. There for an atrractor of the system the largest Lyapunov exponent is computed. The nature of this exponent change allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to the combination of analytical and numerical methods in studying equations of insects population dynamics. At the same time, the analytical approach made it possible to perform numerical analysis in a rather narrow region of the parameter space. It is not possible to get into this area, based only on general considerations.

Keywords: differential-difference equations, asymptotic behaviour, stability, Lyapunov exponents, insect population dynamics.

Funding Agency Grant Number
Russian Science Foundation 14-21-00158
This work was supported by RFBR (project No 14-21-00158).


DOI: https://doi.org/10.18255/1818-1015-2017-3-365-386

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UDC: 517.9
Received: 18.01.2017

Citation: S. D. Glyzin, “Mathematical model of Nicholson's experiment”, Model. Anal. Inform. Sist., 24:3 (2017), 365–386

Citation in format AMSBIB
\Bibitem{Gly17}
\by S.~D.~Glyzin
\paper Mathematical model of Nicholson's experiment
\jour Model. Anal. Inform. Sist.
\yr 2017
\vol 24
\issue 3
\pages 365--386
\mathnet{http://mi.mathnet.ru/mais571}
\crossref{https://doi.org/10.18255/1818-1015-2017-3-365-386}
\elib{http://elibrary.ru/item.asp?id=29332981}


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    This publication is cited in the following articles:
    1. A. Yu. Perevaryukha, “Stsenarii kriticheskoi vspyshki chislennosti invazionnogo vida v modifikatsii uravneniya Gomperttsa”, Vladikavk. matem. zhurn., 21:1 (2019), 51–61  mathnet  crossref
  • Моделирование и анализ информационных систем
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