Dynamic model of population invasion with depression effect

The article is devoted to the study of one of the current scenarios for the development of population processes in contemporary ecological systems. Biological invasions have become extremely common due to climate change, economic activities to improve ecosystem productivity, and random events. The invader does not always smoothly occupy an ecological niche, as in logistic models. The dynamics of the situations we have chosen after the introduction of an alien species is extremely diverse. In some cases, the phenomenon of an outbreak of abundance is quickly realized up to the beginning of the destruction by the species of its new range. The development of the situation in the process of invasion depends on the superposition of biotic and abiotic factors. The dynamics of the abundance of the invader is affected by the favorable conditions and, to a greater extent, by the possibility of realizing the reproductive potential and the resistance of the biotic environment. Counteraction develops with a delay and manifests itself when the invader reaches a significant number. In the work, a continuous model of the invasive process with a sharp transition to a state of population depression has been developed. The stage of the population crisis ends with the transition to equilibrium, since the resistance in the model scenario depends adaptively and in a threshold way on the number. The problem of computational description of a scenario with active but delayed environmental resistance is practically relevant for situations of developing measures of artificial resistance to an undesirable invader. In the solution of our model, there is a mode of prolonged stable fluctuations after exiting the depression stage.