A Continuous Model for Oscillating Outbreak Population of the Phytophagous Moth, Tent Caterpillar, Malacosoma disstria (Lepidoptera, Lasiocampidae)
Outbreaks of individual species population are important phenomena in many aspects and not alike in terms of a theory of multispecies community dynamics. Outbreaks of insect population develop more quickly with long-lasting effects experienced by the forest industry. These events are considered extreme unbalanced and transient processes. The mechanisms of the development and subsidence of insect outbreaks differ in different taxonomic groups of pests. The duration and occurrence of repeated outbreaks of psyllids and forest moths, affecting deciduous or coniferous forests in the same region, are different. Computational simulation is needed for understanding the dynamics of insect outbreaks. For the mathematical description of the outbreaks of forest tent caterpillar, in addition to the threshold version of the development of the insect outbreak, it is interesting to modify the continuous computational models for the analysis of fluctuation dynamics. In this paper, we simulate dynamics of spontaneously damped oscillations under specific scenario during population outbreak using a continuous model with delayed regulation and nonlinear counteraction from the biotic environment. The scenario described by the new phenomenological equation, which consists of a series of different-sized maxima and with a final attenuation of peaks near balance, is realized for the pest tent caterpillar, Malacosoma disstria, which affects deciduous forests in North America leading to large-scale defoliation. The new scenario is qualitatively different from our model of the threshold development and subsidence of outbreaks of the psyllid, Cardiaspina albitextura, in Australia.