ABOUT ONE STOCHASTIC HARVESTING MODEL OF A RENEWED RESOURSE

Abstract

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 x ̇=f(x) and in time moments kd, d>0 from population are taken some random share of a resource ω(k)=(ω_1 (k),…,ω_n (k) )∈Ω, k=1,2,…, that leads to sharp (impulse) reduction of its quantity. Considered resource x∈R_+^n is non-uniform, that is or it consists of separate kinds x_1,…,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.