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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2013, Volume 10, Pages 227–240
(Mi semr410)
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Differentical equations, dynamical systems and optimal control
Asymptotic properties of solutions of nonlinear Sharpe-Lotka model in the most general assumptions
A. N. Pichuginaa, B. Yu. Pichuginb a Omsk State University
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
In the papers [6, 7, 8] based on Sharpe-Lotka model [1, 2] was constructed and studied nonlinear integral model of dynamics of isolated populations with the self-limitation and the finite lifetime of individuals. In 2002 has been proved that the solution of this model has the limit in the case when the equation $\lambda(x) = \beta$ has no more than one root. In this paper we prove that the limit of the solution of the model exists independently of the number of roots of the equation $\lambda(x) = \beta$. In addition, using the results of [9], greatly weakened conditions on model parameters.
Furthermore, the theorem on the continuous dependence on the initial data and the stability theorem was proved.
Keywords:
Sharpe-Lotka model, nonlinear integral equations, renewal equation.
Received October 29, 2012, published March 14, 2013
Citation:
A. N. Pichugina, B. Yu. Pichugin, “Asymptotic properties of solutions of nonlinear Sharpe-Lotka model in the most general assumptions”, Sib. Èlektron. Mat. Izv., 10 (2013), 227–240
Linking options:
https://www.mathnet.ru/eng/semr410 https://www.mathnet.ru/eng/semr/v10/p227
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Abstract page: | 217 | Full-text PDF : | 62 | References: | 34 |
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