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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters

Автор(ы):

Alexander Yur'evich Aleksandrov

Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Control of Medical and Biological Systems, St. Petersburg State University,

a.u.aleksandrov@spbu.ru

Аннотация:

The paper is addressed to the permanence problem for a generalized Lotka-Volterra system modeling interaction of species in a biological community. The impact of a constant delay and switching of parameters on the dynamics of the system is taken into account. Our analysis is based on the Lyapunov direct method. An original construction of a Lyapunov--Krasovskii functional is proposed. The conditions for the existence of such a functional are formulated in terms of feasibility of special systems of linear algebraic inequalities. It is proved that, under these conditions, the investigated system is permanent for any constant positive delay and any admissible switching signal. In addition, a discrete-time counterpart of the considered model is studied for which the permanence analysis is fulfilled, as well. A comparison of the obtained permanence conditions with known ones is provided. It is shown that the constraints on the system parameters derived in this paper are less conservative.

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Ссылки:

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