Perturbed equations for modeling outbreaks during invasive processes

Title	Perturbed equations for modeling outbreaks during invasive processes
Authors	A. Y. Perevaryukha¹ ¹St. Petersburg Federal Research Center RAS
Annotation	Invasive processes in isolated environments represent a complex set of non- linear phenomena of modern ecodynamics with feedback. Occurring after the invasion of a foreign biotic agent (virus, pathogenic microbe or invertebrate) with a reproductive potential that is excessively high for the new environment, it leads to the activation of processes of confrontation with the mutual evolutionary adaptation of the parties – the autochthonous environment and the alien invader. The effect of a destructive outbreak of numbers often develops, which can be prolonged in time and space. In some situations, the invader destroys its environment because adaptation of the resistance is delayed. Two delay factors arise: the replenishment of environmental resources and the delay in developing a response from the environment. The report proposes lagged equations for modeling the evolution of invasions. The models were created taking into account the uncertainty factor in the speed of development of a reaction to the invasion of a dangerous species, but the disturbance is quite limited and never in reality leads to stochastic dynamics of the biophysical process.
Keywords	invasions, adaptations, equations with limited disturbance.
Citation	Perevaryukha A. Y. ''Perturbed equations for modeling outbreaks during invasive processes'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 149-152. Available at: https://conf.svmo.ru/files/2024/papers/paper26.pdf. - Date of access: 16.10.2024.

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Perturbed equations for modeling outbreaks during invasive processes

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