Escape effect and population outbreaks

In this paper we consider the system of mathematical models which describes the interaction of population with its various main regulators and the development of population outbreaks. As a result of these models analysis we obtained the set of different phase portraits which corresponds to the various types of population outbreaks. It was possible to select four different types of outbreaks which were determined in a predator-prey system and in a population-food plant system. For some other models we found the conditions of realization of dynamic regimes of population outbreaks and types of these mass propagations.