Abstracts

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

The nodel Ips Subelongatus Motsch quatity was suggested by Kyselyov V. V. [1,2] for the cases, when natural enemies do not influence it, and when forage being usedby xylophad of generation is usuitable for the settlement of the next generation individuals.

The model may be presented as follows:

,

where t – is a number of generation, N(t)- quantity, P- coefficient of the pest’s survivance (reflects the influence of modifications factors on the dynamics of population), A- supply of forage, x- density of population, - sex corelation in the population, - maximal density of settlement, - minimal density of settlement, - possible constants.

Analysis of model shows, that

when increasing survivance coefficient, the logistical growth of quantity of xylophag changes to oscilation (first – damping, after that - permanent);

when implementing inequity the population degenerates asymptatically at any initial meaning of quantity;

representing carring out of inequity: becomes necessary and suffiiciant of the global stability of permanent point ;

when performing the inequity quantity of population aspires to infinity monotoniously, so far as the volume of entering forage into habitation places of Ips Subelongatus Motsch generation on the period of one generation is constant and quantity of beetles is limited from above by constant (owing to the existence of quite definite of bounds, for the density of settlement), thus we obtain that quantity of migrating beetles from given local habitation place aspires to infinity; the last requireing a grave modification of represented model.

Analysis of ways show, that with increase survivance coefficient in system, may be seen cycles of all low und haos.

Literature:

Esayev A.S., Hlebopros R.G., Nedorezov L.V. Quantity dynamics of forest insects. Novosibirsk: Science, 1984.

Kyseleyv V.V. Analysis of Ips Subelongatus Motsch quantity dynamics. Abstract of thesis. Krasnoyarsk, 1978

Note. Abstracts are published in author's edition

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