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JOURNALS // Matematicheskoe modelirovanie // Archive

Mat. Model., 2009 Volume 21, Number 8, Pages 3–20 (Mi mm2862)

Stabilization and vitality in ecological models. Formation process of passive states

V. G. Il'ichev

Southern Scientific Centre of Russian Academy of Science, Rostov-on-Don

Abstract: We formalize the individual biological transition process from an active to a passive state under unfavor-able environment conditions. From the mathematical point of view this leads to an universal linear super-structure over nonlinear ecological system models. We infer that under a special choice of transition ve-locities there is a possibility of oscillatory instability stabilization and of an increasing of populations vital-ity. The correct models of adaptation of biological coefficients in variable environment, taking into ac-count the “active state–passive state” interchange are offered. In the model “prey–predator” the cycle movement (chasing–escape) within the space of parameters is revealed.

Received: 07.08.2007



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