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

V. G. Il'ichev

Matematičeskoe modelirovanie, Tome 21 (2009) no. 8, pp. 3-20

Résumé

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.