ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Frisman E. Y., Neverova G. P., Revutskaya O. L., Kulakov M. P. Dynamic modes of two­-age population model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 2, pp. 113-130. DOI: 10.18500/0869-6632-2010-18-2-113-130

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Language: 
Russian
Heading: 
Nonlinear Dynamics in Action
Article type: 
Article
UDC: 
517.958:57
DOI: 
10.18500/0869-6632-2010-18-2-113-130

Dynamic modes of two­-age population model

Autors: 
Frisman Efim Yakovlevich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Neverova Galina Petrovna, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Revutskaya Oksana Leonidovna, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Kulakov Matvej Pavlovich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Abstract: 

In this paper we research a mathematical model of dynamics for the population number. We considered the population of the two-age classes by the beginning of the next season: the younger, one including not reproductive individuals, and the senior class, consisting of the individuals participating in reproduction. The model parameters (birth rate and survival rates) represent the exponential functions of the both age groups numbers. According to this supposition the density-dependent factors restrict the development of population. Analytical and numerical analysis of the model is made. We investigate the dynamic modes of the model. It is shown that density-dependent factors of regulation for the population number can lead to generation of fluctuations and chaotic dynamics behavior of the population.

Key words: 
Population models equations
discrete-time systems
age distribution
densitydependent
stability
bifurcations
dynamic modes
chaos
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Received: 
29.05.2009
Accepted: 
06.10.2009
Published: 
30.04.2010
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