Phenomenological Computational Model for the Development of a Population Outbreak of Insects with Its Bifurcational Completion

Perevaryukha, A. Yu.

doi:10.1134/s2070048218040117

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…Ограничивающий показатель воздействия J, N(t) < J, ∀t, 0 < N(0) < J, в уравнении ( 14) зеркально симметричен по смыслу критическому порогу L из уравнения А. Д. Базыкина как нижней грани для существования локальной популяции 0 < N(0) < L, lim t→∞ N(t) = 0. В развитии модели логично представить, что J не является константой, но, возможно, станет ступенчатой триггерной функцией [Perevaryukha, 2018]. Например, в простом варианте порог J колеблется от смены сезонов по периодическому закону J(ω(t)).…”

Section: компьютерные исследования и моделированиеunclassified

Models of population process with delay and the scenario for adaptive resistance to invasion

Perevarukha¹

2022

CRM

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Changes in abundance for emerging populations can develop according to several dynamic scenarios. After rapid biological invasions, the time factor for the development of a reaction from the biotic environment will become important. There are two classic experiments known in history with different endings of the confrontation of biological species. In Gause's experiments with ciliates, the infused predator, after brief oscillations, completely destroyed its resource, so its r-parameter became excessive for new conditions. Its own reproductive activity was not regulated by additional factors and, as a result, became critical for the invader. In the experiments of the entomologist Uchida with parasitic wasps and their prey beetles, all species coexisted. In a situation where a population with a high reproductive potential is regulated by several natural enemies, interesting dynamic effects can occur that have been observed in phytophages in an evergreen forest in Australia. The competing parasitic hymenoptera create a delayed regulation system for rapidly multiplying psyllid pests, where a rapid increase in the psyllid population is allowed until the pest reaches its maximum number. A short maximum is followed by a rapid decline in numbers, but minimization does not become critical for the population. The paper proposes a phenomenological model based on a differential equation with a delay, which describes a scenario of adaptive regulation for a population with a high reproductive potential with an active, but with a delayed reaction with a threshold regulation of exposure. It is shown that the complication of the regulation function of biotic resistance in the model leads to the stabilization of the dynamics after the passage of the minimum number by the rapidly breeding species. For a flexible system, transitional regimes of growth and crisis lead to the search for a new equilibrium in the evolutionary confrontation.

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Section: компьютерные исследования и моделированиеunclassified

Models of population process with delay and the scenario for adaptive resistance to invasion

Perevarukha¹

2022

CRM

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“…Mikhaylov used models based on algorithmic networks with thousands of nodes [11]. Our models can be calculated by using simple free program tools such as a laptop and a computational workbench tool Rand Model Designer [12].…”

Section: Mathematical Improvement Of a Biological Theory Of The Replenishment Of Stocks Formationmentioning

confidence: 99%

Development and scenario experiments with the new model of rapid bioresources crisis under expert control

Perevaryukha¹

2021

MMS

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This paper continues a series of studies dedicated to the analysis of the nonlinear dynamics of complex environmental processes through the use of computational methods. The construction of a computational structure that uses the forms of the hybrid time and the logic of redefined behavior of solutions of the special system of equations to describe important nonlinear phenomena in the man-agement of unstable biosystems is considered in the article. The difference between the described ap-proaches to building a model is that computational experiments based on differential equations and re-defined according to the rules simulate scenarios in the dynamics of controlled biological resources of different types. The form of time allows to operate on a discrete component of the trajectory to describe changes that are visible to experts from the monitoring statistics or from reports from the fishery. The computational structure logically corresponds to the life cycle of large marine fish. Continuous characteristics are used to manage changes in the life cycle model. The new models are intended to de-scribe in scenarios the phenomena of rapid degradation of valuable biological resources with a very small error in the regulation of the rate of removal from the stock. These models have shown that the tradi-tional methods of bioresources management by experts have fundamental shortcomings and problems. Experts overestimate the amount of stocks for commercial removal from the population. Regulation by setting quotas on fish catch does not prevent the fishery from collapsing. The approach is applicable for mathematical predicting of the rapidly inflowing phases of an ecological invasion in aquatic systems.

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Scenario Modeling of the Collapse of Red King Crab Stocks under the Expert Control of the Annual Catch

Perevaryukha

2022

Math Models Comput Simul

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Phenomenological Computational Model for the Development of a Population Outbreak of Insects with Its Bifurcational Completion

Cited by 5 publications

References 12 publications

Models of population process with delay and the scenario for adaptive resistance to invasion

Models of population process with delay and the scenario for adaptive resistance to invasion

Development and scenario experiments with the new model of rapid bioresources crisis under expert control

Scenario Modeling of the Collapse of Red King Crab Stocks under the Expert Control of the Annual Catch

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