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Dynamic Model of Population Invasion with Depression Effect

The article is devoted to the study of one of the current scenarios for thedevelopment of population processes in contemporary ecological systems. Biological invasionshave become extremely common due to climate change, economic activities to improve ecosystemproductivity, 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 analien species is extremely diverse. In some cases, the phenomenon of an outbreak of abundanceis quickly realized up to the beginning of the destruction by the species of its new range. Thedevelopment of the situation in the process of invasion depends on the superposition of bioticand abiotic factors. The dynamics of the abundance of the invader is affected by the favorableconditions and, to a greater extent, by the possibility of realizing the reproductive potential andthe resistance of the biotic environment. Counteraction develops with a delay and manifests itselfwhen the invader reaches a significant number. In the work, a continuous model of the invasiveprocess with a sharp transition to a state of population depression has been developed. The stageof the population crisis ends with the transition to equilibrium, since the resistance in the modelscenario depends adaptively and in a threshold way on the number. The problem of computationaldescription of a scenario with active but delayed environmental resistance is practically relevantfor situations of developing measures of artificial resistance to an undesirable invader. In thesolution of our model, there is a mode of prolonged stable fluctuations after exiting the depressionstage.