Scenarios of the passage of the «population bottleneck» by an invasive species in the new model of population dynamics

Topic. The subject of the article is the expansion of the author’s research series in the direction of mathematical modeling of specific ecological situations and transitional regimes that arise in nonlinear population processes with complex internal regulation. Aim. The purpose of the article is to develop methods for modeling difficult-to-predict and abrupt changes in the ecology of communities of competing species. Such events occur after the invasion and adaptation of a species with a potentially high reproductive potential to a new area with favorable reproduction conditions. Relevance. The significance of the environmental problem we are considering based on the fact that when developing a rapid outbreak of insect, ordinary and easily mathematically formalized principles for regulating the efficiency of population reproduction do not work. In scenarios related to the manifestation of extreme population dynamics, traditional models of mathematical biology for describing asymptotic growth of populations or stable oscillatory regimes will not be applicable. Method. Activation of inclusion in the active counteraction for aggression is often significantly delayed, therefore, differential equations with delay are chosen by the mathematical description of transient situations. We believe in the development of new models that outbreaks of populations are a group of phenomena that are heterogeneous in their dynamic characteristics, stages and causes. The outbreaks of Hemiptera's insects differ in terms of phases and duration from invasions of Lepidoptera pests. Variants of development and completion of outbreaks differ. Result. The main result of our work will be a model scenario based on modifications of differential equations with delay, when after invasive invasion the invading species passes through the «bottleneck mode» – of a critically small group of individuals, capable of further survival only under favorable conditions. We solved the problem of bottleneck in the population dynamics when considering in the modification of the active counteraction model of invasion, it is assumed that the undesirable species is able to substantially transform its new biotic environment. Discussion. One of the considered computational scenarios leads to the destruction of the cyclic regime that appeared in the equation, which reflects the elimination of the dangerous competitor species from the new habitat. Real biological processes of insect dynamics provide for several variants of final paths. An alternative version of the scenario obtained by us in the modification of the equation with independent withdrawal is the completion of the outbreak of the alien species with the formation of a stable small group, perhaps in the hidden shelter for the so-called «refugium mode».