• Title/Summary/Keyword: Mathematical Ecology

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Mathematical models for population changes of two interacting species (상호작용하는 두 생물 종의 개체 수 변화에 대한 수학적 모델)

  • Shim, Seong-A
    • Journal for History of Mathematics
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    • v.25 no.1
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    • pp.45-56
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    • 2012
  • Mathematical biology has been recognized its importance recently and widely studied in the fields of mathematics, biology, medical sciences, and immunology. Mathematical ecology is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats. It was the earliest form of the research field of mathematical biology and has been providing its basis. This article deals with various form of interactions between two biological species in a common habitat. Mathematical models of predator-prey type, competitive type, and simbiotic type are investigated.

A study on mathematical models describing population changes of biological species (생물 종의 개체 수 변화를 기술하는 수학적 모델에 대한 고찰)

  • Shim, Seong-A
    • Journal for History of Mathematics
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    • v.24 no.2
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    • pp.47-59
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    • 2011
  • Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

Dynamic Customer Population Management Model at Aggregate Level

  • Kim, Geon-Ha
    • Management Science and Financial Engineering
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    • v.16 no.3
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    • pp.49-70
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    • 2010
  • Customer population management models can be classified into three categories: the first category includes the models that analyze the customer population at cohort level; the second one deals with the customer population at aggregate level; the third one has interest in the interactions among the customer populations in the competitive market. Our study proposes a model that can analyze the dynamics of customer population in consumer-durables market at aggregate level. The dynamics of customer population includes the retention curves from the purchase or at a specific duration time, the duration time expectancy at a specific duration time, and customer population growth or decline including net replacement rate, intrinsic rate of increase, and the generation time of customer population. For this study, we adopt mathematical ecology models, redefine them, and restructure interdisciplinary models to analyze the dynamics of customer population at aggregate level. We use the data of previous research on dynamic customer population management at cohort level to compare its results with those of ours and to demonstrate the useful analytical effects which the precious research cannot provide for marketers.

A Historical Study on the Representations of Diffusion Phenomena in Mathematical Models for Population Changes of Biological Species (생물 종의 개체 수 변화를 기술하는 수학적 모델의 확산현상 표현에 대한 역사적 고찰)

  • Shim, Seong-A
    • Journal for History of Mathematics
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    • v.29 no.6
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    • pp.353-363
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    • 2016
  • In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.

A thought experiment on the Cochlodinium bloom in Korean waters (한국해역 Cochlodinium의 이상증식에 대한사고실험)

  • 이동섭
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.9 no.4
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    • pp.173-178
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    • 2004
  • Chronic Cochlodinium blooms in the southern waters of Korea have brought about considerable economic losses for about a decade, This paper aims to reframe current perspectives on the outbreak mechanism and the remediation schemes through a thought experiment in a context of mass balance and mathematical ecology. Far different explanations emerge from a careful examination of the scientifically unnoticed clues and a through discussion on the phytoplankton conservation equation. Logic of the eutrophication-induced red tide subjects to criticism. It is strongly recommended that the current remediation scheme to exterminate the target species should be rerouted to an environmentally sound competition enhancement tactics. Finally a novel convergence-float-aggregation hypothesis is proposed as an outbreak mechanism.