By carrying out a theoretical synthesis of the information on the regularities of population dynamics of some insect pests of agricultural plants and based on the past and present the authors have analysed the dynamics of many years in the number of the insect populations. An attempt to determine the presence of synchronism of outbreaks of the insects’ mass reproduction with the years of sharp changes in the solar activity has been made; the relationship between the changes in the number of the insects and meteorological and heliographic factors has been analysed. An analysis of the dynamics of the sun pest reproduction taking into account the duration of sunshine on the materials of one of the outbreaks (local population) in the Kupiansk district of the Kharkiv region showed the unreliability of this index as a predicate of the prognosis; and the reproduction rate of the local population of the sun pest does not change depending on the duration of the solar radiance. It is determined that this principle is also unsuitable for forecasting the dynamics in the number of this pest. The linear differential equations, in which not only the meteorological factors but also the indices of the solar activity (global factor) were used as variables were unsuitable for prognostication the dynamics in the number of the insects. The examples listed in the article confirm the fundamental regularity, namely the polycyclic dynamics of various natural systems and the synchronism in their development. The synchronization is inevitable because all objects of inanimate and living nature consist of the same chemical elements, and the conservation and conversion of energy is universal in nature. Based on the methodology of the cyclic dynamics it is possible to develop the algorithms for prognostication the regular mass reproduction of harmful insects.

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The authors have analysed the theoretical possibilities of prognostication the dynamics in the number and mass reproduction of some species of harmful insects. A theoretical synthesis of the information on the regularities of the population dynamics of the most common insect pests of agricultural plants from the point of view of the methodology of nonlinear dynamics and synergetics has been done. Based on the past and present an analysis of the many-year dynamics in the number of the insect populations has been carried out and an attempt to develop the algorithms for prognostication the seasonal and annual changes in the number of the insects has been made. To do this the authors recommend a scenario-based method of prognostication and making decisions in plant protection. Using the phytosanitary monitoring they determine the beginning of the regular mass reproduction (the appearance of an aggravated rate) and then, based on the phytosanitary prognosis, an aggravation of the situation that has developed or is being developing on the farm, in the district or in the region is made; after that on the base of the short-term prognosis (signaling) it is recommended to make the optimal decision to protect a particular crop taking into account the economic threshold of harmfulness. According to the authors this approach, based on the methodology of nonlinear dynamics (synergetic paradigm), makes it possible to determine in advance the breeding grounds of the aggravated rates and make the optimal decisions in plant protection. The predicted scenario will not be a prognostication of the future, but the elements of an evolutionary process inherent in nature.