Журнал «Труды Института системного анализа Российской академии наук» - A.Y. Perevaryukha Model for the scenario of bioresources depletion under expert management of exploitation strategy

We have developed a scenario approach for modeling natural processes under controlled anthropogenic impact. Determining a rational exploitation strategy for large predator species remains one of the controversial problems, and weakly formalized expert methods of fishery management are used for this task. Methods for determining commercial withdrawal quotas for other biological resources, which have previously worked successfully for some objects, can lead to long-term degradation of populations. We have developed a model of population reproduction with a hybrid time and with an algorithm that changes the regulation function depending on the current state of the stock. On the basis of the proposed computational model and typical logic of decisionmaking when changing the fishing impact, an oscillating scenario of collapse is considered on the example of red king crab Paralithodes camtschaticus. The dynamics of the new model with sharp fluctuations in abundance leads to the collapse of the fishery, when experts can expect a recovery of these stocks. The scenario model uses transformations of the phase portrait: disconnected boundaries of the attraction basins of attractors and a strange repeller, direct and inverse tangent bifurcations of stationary points, an attractor in the form of a set of disconnected intervals. Stochastic effects arise in this deterministic population model.