Abstract:
Our studies are devoted to various aspects of invasive processes in biosystems. When invading aggressive insects, the resistance of the biotic environment is significant, but the final time may be completely absent. Under conditions of high specific fecundity, there will be non-stationary regimes of changes in the abundance of individuals in the population. An outbreak with a phase of explosive growth is realized, so we modeled one particular variant of an outbreak of populations earlier. Outbreaks are associated with a number of changes in physiological regulation that are observed in ecodynamics under extreme conditions of the species and environment. A classic example of changes is the appearance of migratory winged forms in the locust and the usually flightless leaf beetle introduced in the Stavropol Territory Zygogramma suturalis during the formation of a population wave front with a huge density of individuals. Traditional mathematical models for describing the rates of average weight gain for individuals of a generation cannot consider situations of rapid invasions, where competition and survival factors at different stages of insect development are very different, since the density of generations varies by orders of magnitude. Effect on growth of local congestion value may not be constant in ontogenesis. The factor of the total number is reflected differently at different stages of life. The purpose of the simulation is to obtain a bistable and flexible dynamic system. The article proposes a model for a differentiated description of weight gain at three stages of development of insects with an incomplete cycle of transformations by three differential equations conjugated by initial conditions. As a result, a continuously discrete dynamic system with a hybrid representation of time on the life cycle interval is implemented. We will use the model when supplementing the hybrid computing structure for calculating the rate of decline of individuals of generations. Mortality changes dramatically with the launch and attenuation of an invasive outbreak. Here, the deviation of growth rates from optimal values plays a role. The idea of the work is that all processes: changes in numbers or growth for insects should be simulated by the stages of development of their ontogenesis.
Keywords:models of population dynamics, invasion, insect outbreaks, growth models, stages of ontogenesis, hybrid systems, Allee effect, bifurcations and cycles, cognitive graphs, extinction of biological species.
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