Phenomenological Computational Model for the Development of a Population Outbreak of Insects with Its Bifurcational Completion

Abstract

The article discusses the model scenario of a sharp increase in the number of phytophagous insects, a dangerous and poorly predictable phenomenon. The scenario is based on the possibility of an increased reproduction efficiency of the state of the population in the range limited from above and from below. A time-limited local outbreak begins after overcoming the threshold equilibrium point. The slowdown in the rate of loss of generations is caused by the attenuation of the customary mechanisms of density regulation. The developed redefined computational structure takes into account the structure of various vulnerabilities of life stages before entry into the fertile age, which is established for the European corn borer. Reduction of the role of mortality factors will be unevenly distributed in the ontogenetic stages of the insect. The sudden start of the regulation mechanism due to the exhaustion of resources, which is strengthened because of the indirect competition between the adult and larval stages, is implemented by a special supplement on the right side in the equation of the population size decrease. The described variable effect of mortality regulation leads to a tangential bifurcation, which completes the phase of uncontrolled reproduction. In conclusion, we consider an example of a real situation of spontaneously decaying outbreaks of a pest vulnerable for its enemies corresponding to the derived characteristics of a dynamical system.