Affiliation:
1. Vladimir State University; Mai-Nefhi College of Science
2. Vladimir State University; National University of Science and Technology MISIS
Abstract
We consider a population whose dynamics in the absence of exploitation is given by a system of linear homogeneous differential equations, and some random shares of the resource of each species at fixed times, are extracted from this population. We assume that the harvesting process can be controlled in such a way as to limit the amount of the extracted resource in order to increase the size of the next harvesting. A method for harvesting a resource is described, in which the largest value of the average time benefit is reached with a probability of one, provided that the initial amount of the population is constantly maintained or periodically restored. The harvesting modes are also considered in which the average time benefit is infinite. To prove the main assertions, we use the corollary of the law of large numbers proved by A.N. Kolmogorov. The results on the optimal resource extraction for systems of linear difference equations, a particular case of which are Leslie and Lefkovich population dynamics models, are given.
Subject
General Medicine,Linguistics and Language,Language and Linguistics,Education,General Decision Sciences,Public Health, Environmental and Occupational Health,Orthopedics and Sports Medicine,Physical Therapy, Sports Therapy and Rehabilitation,Education,General Medicine,General Medicine,General Physics and Astronomy,Cell Biology,Plant Science,Molecular Biology,Biochemistry,Biotechnology