Phenomenological computational models for passing outbreaks of insects with its bifurcation completion

The article discusses the model scenario of sharp increase in the number of insect phytophage, dangerous and poorly predictable phenomenon. The scenario based on possibility of increasing the efficiency of reproduction in the limited range of operation of the population. Time-limited local outbreak begins after overcoming the threshold in the form of an equilibrium point. Insect generations decrease rate slows, due to attenuation the customary mechanisms of death regulation that depends on the density of the pests. In the developed redefined computing take into account the structure of various vulnerable life stages before entry into fertile age, which is established for the European corn borer. Reducing the role of mortality factors it is unevenly distributed in the ontogenetic stages of the insect. Sharp inclusion mechanism of regulation of the exhaustion of resources, which is heavily because of the indirect competition between adult and larval stages, implemented by special supplement on the right side in the equation of generation mortality dynamics. We have described a variable effect of mortality regulation leads to a tangent bifurcation, which completes the phase of uncontrolled reproduction. In conclusion, we consider the corresponding dynamical system derived characteristics example of a real situation spontaneously decaying pest outbreaks.