A model of development of a spontaneous outbreak of an insect with aperiodic dynamics

Perevaryukha, A. Yu.

doi:10.1134/s0013873815030124

Cited by 8 publications

(3 citation statements)

References 11 publications

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“…A transition to sawtooth-like fluctuations is observed in pests, as mentioned above. The scenario with short Λ-shaped outbreaks in aphids and psyllids requires other attractor modifications [66]. The dynamics of model (10) do not describe the case where acute virus infection develops into chronic disease because a high virus load is maintained for a long period of time in the vicinity of unstable equilibrium (a developmental threshold) in this scenario.…”

Section: Representation Of a Delay In The Regulatory Functionalmentioning

confidence: 99%

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

Perevaryukha

2021

BIOPHYSICS

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This article focuses on the modeling of crisis and threshold development of the population process during the formation of a new population in a competitive environment. As a population spreads, a deep population crisis may arise as a result an abrupt triggering of biotic countermeasures before resources for a further increase in population size are exhausted. A bottleneck occurred in the history of many populations, including humans at the time of the Neolithic crash in Europe. Invaders with high reproductive potential often exert deleterious effects on biosystems. The emergence of efficient competition can not only cause classical cyclical fluctuations, but also lead to a complete extinction of the population after a series of high peaks in its abundance. Two alternative scenarios provide classical examples of induced population crises. One was observed in Gause's experiments where an introduction of a predatory ciliate drove another ciliate species to extinction. The other scenario was observed in a series of experiments where bacteriophages were introduced into colonies of actively dividing bacteria that had a dynamically adapting antiviral mechanism. In this work, modifications to the model were proposed to describe the actual scenarios of crisis effects in population dynamics. Equations with deviating arguments in the time variable allowed a threshold effect of conditions on reproduction of the invasive species and an aggregated nature of the lagging regulation with two time factors. The computational scenarios described both completion of the process after a repeated outbreak and successful elimination of the population crisis via rapid adaptation. Deep crisis phenomena are characteristic of local population dynamics when organisms interact with viruses that are new to them.

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Section: Representation Of a Delay In The Regulatory Functionalmentioning

confidence: 99%

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

Perevaryukha

2021

BIOPHYSICS

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“…По решаемым задачам математические методы популяционной биологии можно разделить на прикладные модели (оценки эксплуатации биоресурсов или роста организмов) и уравнения системных процессов в теоретической экологии (переноса энергии по уровням, развития сукцессии). Наиболее актуальная ранее задача моделирования оптимизации эксплуатации, максимизации прибыли от объекта промысла, теряет значимость после ряда коллапсов, как, например, ситуации с треской Лабрадора [19] и осетровыми рыбами Каспийского моря [18]. В современных работах концепция Maximum sustained yield, которая предполагает полное изъятие «излишков» рыбного запаса, подвергается критике из-за повышения рисков кризиса.…”

Section: существующие методы описания нестационарных популяционных реunclassified

Oscillation and Extinction Scenarios in the New Continuous Model of the Eruptive Phase of Alien Species Invasion

Perevaryukha

2019

MPCS

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The paper considers the issue of modeling the development of those special population processes that include the passage of the eruptive phase of dynamics. Such brief hurricane regimes of change are often associated with the consequences of invasions of undesirable species. Processes in the introduction of a species can often develop through the delayed phase of a rapid increase in its abundance. The completion of the phase depends on many factors. Outbreaks of many species exert such a strong pressure on the environment that achieving a non-zero balance equilibrium is problematic. Such phenomena are interpreted by us as an extreme transition process to an uncertain state of the biotic environment before the beginning of the process. Depending on the counteraction, which is clearly seen in the examples of the dynamics of insect pests, simulated scenarios of similar phenomena can develop in various ways, including destruction of the habitat. The new model based on the equation with a deviating argument describes the variant of developing the repeated flash of catastrophic character. The scenario is implemented when non-harmonic cycle N*(rτ, t) occurs, which can not be orbitally stable under the given conditions, but becomes transitive. The cycle ends with the trivial-zero value. The scenario of the most abrupt form of the eruptive phase that we simulate ends in a computational experiment by the death of the invasive population, but without forming an unbounded trajectory from the oscillations, as was the case with the destruction of the relaxation cycle of the extreme amplitude in the population flash equation in our previous work.

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“…Предложенная нами ранее непрерывно-дискретная модель с апериодической динамикой описывает только один из возможных сценариев вспышки тропической популяции с бифуркационным за-вершением [11]. Одним из интересных явлений представляется возникновение всплес-ков негармонических флуктуаций у насекомых-вредителей.…”

Section: Introductionunclassified

Destruction of the Relaxation Oscillations in the Model of Extreme Dynamics of the Population

Perevaryukha¹

2017

Vestn. Volgogr. gos. univ., Ser. 1. Math. Phys.

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Кандидат технических наук, cтарший научный сотрудник, Санкт-Петербургский институт информатики и автоматизации РАН temp_@mail.ru 14-я линия Васильевского острова, 39, 199178 г. Санкт-Петербург, Российская Федерация Аннотация. В контексте моделирования нетривиальных перемен в раз-витии популяционных процессов предлагается уравнение с запаздыванием = λ ( ) ( ( − τ))ψ( ( − τ)), где λ, > 0, ψ( ) -меняющая знак функция. В новой модели трактовка предпороговой емкости среды отличается от асимп-тотического балансового равновесия ( ) → из уравнения Ферхюльста -Пирла. Вычислительное исследование потери устойчивости особой точки по-казывает помимо известного сценария образования глобального орбитально устойчивого цикла в логистическом уравнении с запаздыванием другой вари-ант метаморфоза -с разрушением возникших при изменении репродуктив-ного параметра неустановившихся релаксационных колебаний и появлением неограниченного сверху псевдопериодического решения. При возрастании ам-плитуды релаксационных колебаний сценарий катастрофического завершения фазы роста численности популяции реализуется в зависимости не от достиже-ния критического минимума, а от положения максимума в случае превыше-ния нестабильной популяцией допустимой поддерживающей емкости среды. Модель применима для описания вспышек численности ряда биологических видов, сильно воздействующих на пригодность среды своего размножения.Ключевые слова: модели популяционных колебаний, уравнения с запаз-дыванием, регулярные циклы и вспышки численности, редкие экологические сценарии, пороговые ситуации.

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A model of development of a spontaneous outbreak of an insect with aperiodic dynamics

Cited by 8 publications

References 11 publications

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

Oscillation and Extinction Scenarios in the New Continuous Model of the Eruptive Phase of Alien Species Invasion

Destruction of the Relaxation Oscillations in the Model of Extreme Dynamics of the Population

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