About one stochastic harvesting model of a renewed resourse

L. I. Rodina

Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 685-695

Résumé

We investigate the models of dynamics of the harvested population, given by the control systems with impulse influences depending on random parameters. We assume that in the absence of harvesting population development is described by system of the differential equations $\dot x =f (x)$ and in time moments $kd, $ $d> 0$ from population are taken some random share of a resource $ \omega (k) = (\omega_1 (k), \ldots, \omega_n (k)) \in \Omega, $ $k=1,2, \ldots, $ that leads to sharp (impulse) reduction of its quantity. Considered resource $x\in\mathbb R^n _ + $ is non-uniform, that is or it consists of separate kinds $x_1, \ldots, x_n, $ or it is divided on $n $ age groups. In particular, it is possible to assume that we make harvesting of $n $ various kinds of fishes between which there are competition relations for food or dwelling places. We describe the probability model of a competition of two kinds for which we receive the estimations of average time benefit from the resource extraction, fulfilled with probability one.

Détail

Keywords: model of the population subject to a craft, average time profit
Mots-clés : optimal exploitation.