Abstracts

Evolution of Species and Ecosystems: Theoretical Analysis and Computer-Assisted Modeling

At present work there is the consideration of population dynamics model of spruce budworm (Choristoneura fumiferana). The basic model is a system of ordinary differential eguations with impulses. In this model we took into consideration the influence of pathogens onto the population dynamics which is one of the most important regulators of larvae density:
, ,
, ,
, ,
,

where is a density of young healthy larvae, is a density of young sick larvae, is a density of pupae, is a density of morth, is a density of old healthy larvae, is a density of old sick larvae, are the coefficients of natural mortality, are the coefficients of self-regulation, are the natural mortality coefficients, are the lengths of respective phases of insects, is a coefficient of reproduction, is a part of survived insects after winter period.

Analysis of this model allowed to obtain the following results:
1. Under all nonnegative initial data solutions are limited and nonnegative.
2. If the following condition is satisfied
.
the population degenerates under all initial conditions.
3. The numerical analysis of the model showed that there are the following regimes can be realized: cyclic population behaviour (with various periods) and stabilization of population. Thereby, the influence of pathogens onto the dynamics of spruce burdworm density can lead to cyclic behaviour. It is necessary to note that oscillation regimes are absent in model if there are not pathogens in a system. In some cases the oscillation regimes have the features which are similar with considering in a nature. Publication is supported by RFFI grant 01 - 04 - 48965.

Note. Abstracts are published in author's edition

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