Comparative Analysis of the Results of Modeling of Extreme Population Processes for Fish and Insects

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Situations of sharp short-term changes in population processes can not be calculated by traditional mathematical models — a system for balance equilibrium. Unstable and short time shifts can not be expressed in terms of asymptotic dynamics — closed limit sets of the trajectory, stable cycles or even chaotic attractors. In our studies, it is carried out computational modeling of practically important scenarios of outbreaks and dangerous invasions related to extreme and transient dynamics. Ecosystems, like organisms, can not last for long in such transitional regimes. Outbreaks of the number of harmful insects in the form of individual peaks but not oscillating regimes have a number of features of threshold development. Unexpectedly, the problem of analysis of outbreaks intersects with the problem of modeling depletion of stocks in the fishery of fish. Rapid degradation of population size in the collapse scenarios could not be predicted in time by the methods of calculating the catch quotas (shown on examples of cod of the North Atlantic and anchovy of Peru), because the rates of restoration of reserves were incorrectly estimated. A key aspect in the methodology for constructing hybrid models is the formalization of nonlinear reproduction efficiency, which varies in a threshold manner. In the article it is proved the advantages of the method of purposeful realization of bifurcations in hybrid systems. It has been carried out the comparative analysis of new model scenarios for extreme situations with similar phases during the collapse of fish stocks and insect outbreaks of pests obtained by modifying functional in the basic hybrid system. Five variants of qualitative behavior of hybrid systems that are important for modeling of biosystems were identified.