Dynamics of Forest Insect Density: Bifurcation Approach

Abstract

Six basic phase portraits differing in character and in the number of their equilibrium behaviour regimes were suggested in the classification of forest insect population dynamics. The portraits graphically illustrate six types of dynamic behaviour of numbers of the system “phytophage-entomophage”: two types of stable equilibrium dynamics (stationary and oscillatory) and four types corresponding to outbreaks of mass reproduction—fixed, permanent, reversive and true outbreaks, respectively.In this paper we consider the single parameter model, with its parametric domains realizing a wide spectrum of phase dynamics, both basic and transitional. The changes in the phase portraits are accompanied by the bifurcations in the model.The results of these analyses are in agreement with the “stability principle of mobile ecological systems” and may supply its parameter substantiation at the model level.