Scenarios of critical outbreak of invasive species in new modification of Gompertz

The paper discusses the problem of modeling the variants of the development of situations of extreme type in the population process that can arise due to the propagation of alien species. For mathematical formalization of phenomena, equations with a delay argument are used. In the above-mentioned environmental context, it is interesting to consider not the occurrence of cycles or the properties of stable oscillation modes in the solution of such equations. We urgently need to search for specific transitional scenarios of population dynamics. A series of modifications based on the Gompertz equation is proposed successively, as proved to be more suitable for improvement than the Hutchinson or Nicholson models. In models involving the function of the resistance of the biotic environment, scenarios of the death of the population after the outbreak were obtained. An alternative variant of the numerical scenario is the formation of a stable small group with the passage of the permissible barrier number of adults in the population...