• Journal for History of Mathematics
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• v.33 no.3
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• pp.167-177
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• 2020

Cooperative behavior may seem contrary to the notion of natural selection and adaptation, but is widely observed in nature, from the genetic level to the organism. The origin and persistence of cooperative behavior has long been a mystery to scientists studying evolution and ecology. One of the important research topics in the field of evolutionary ecology and behavioral ecology is to find out why cooperation is maintained over time. In this paper we take a historical overview of mathematical models representing cooperative relationships from the perspective of mathematical biology, which studies population dynamics between interacting biological groups, and analyze the mathematical characteristics and meanings of these cooperative models.

• Journal of Korea Technology Innovation Society
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• v.6 no.2
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• pp.213-227
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• 2003

초고속 인터넷 서비스는 사용자수의 증가와 더불어 고객의 다양한 욕구 즉 인터넷 방송, 주문형비디오(VOD)서비스, 원격교육, 고화질 TV 등 대용량의 멀티미디어 서비스에 대한 욕구가 폭발적으로 증가하고 있다. 이러한 욕구를 충족하기 위해서는 현재의 초고속 인터넷서비스로서는 속도에 대한 한계에 부딪치게 되어 통신사업자들은 새로운 기술 또는 여러 가지 기술적 대안들을 추구하고 있다. 2002년부터 시작하여 2003년 이후에는 멀티미디어 수요의 증가에 따라 ADSL을 대체하는 기술로 VDSL이 등장하여 매년 꾸준한 신규가입자 수요가 발생하고 있으나, 통신사업자들은 각각의 망 특성, 시장위치, 전략적 필요성 둥에 의해 상용화를 적극 검토,추진하고 있으나 각각 전개하는 방식은 조금씩 다르다. 따라서 본 연구에서는 통신사업자들의 가입자망 진화 전략에 대해 살펴 본 다음 Lot3n-Volterra Competition (LVC) 모델을 이용 ADSL 과 VDSL 두 기술간의 상호 경쟁 및 대체를 통해 어떻게 진화 되어가는지를 살펴보았다. 대표적인 통신사업자인 KT는 막강한 자금력을 바탕으로 시장 확대 및 경쟁사와의 차별화를 위해 VDSL 서비스 조기도입을 서두르고 있고, 하나로는 자금의 열세로 인한 ADSL 투자비를 회수 할때까지 VDSL 서비스를 연기하고 있는 실정이다. ADSL과 VDSL 두 기술의 관계는 Lotka-Volterra Competition (LVC) 모델을 이용한 시뮬레이션 결과를 통해 빠른 속도와 비슷한 가격대의 VDSL이 침략자(predator)로 기존 시장 지배자인 ADSL을 사냥감(prey)으로 빠른 속도로 대체해 나가는 것을 알 수 있었다.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.4
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• pp.297-303
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• 2011

Major ports in Northeastern Asia engage in fierce competition to attract transshipment traffic volume. Existing time series analyses for analyzing port competition relationships examine the types of competition and relations through the signs of coefficients in cointegration equations using the transshipment traffic volume results. However, there are cases for which analyzing competing relationships is not possible based on the results of the transshipment traffic volume data differences and limitations in the forecasting of traffic volume. Accordingly, we used the Lotka-Volterra (L-V) model,also known as the ecosystem competitive relation model, to analyze port competition relations for the long-term forecast of South Korean transshipment traffic volume.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.197-210
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• 2013

The late 18C Malthus studied population growth for the first time, Verhulst the logistic model in 19C and, after that, the study of the predation competition between two species resulted in the appearance of Lotka-Volterra model and modified model supported by Gause's experiment with bacteria. Instable coexistence equilibrium being found, Solomon and Holling proposed functional and numerical response considering limited abilities of predator on prey, which applied to Lotka Volterra model. Nicholson and Baily, considering the predation between host and parasitoid in discrete time, made a model. In 20C there were developed various models of disease dynamics with the help of mathematics and real data and named SIS, SIR or SEIR on the basis of dynamical phenomena.

• Journal of the Korea Society for Simulation
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• v.29 no.4
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• pp.9-19
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• 2020

The number of customers on Social Network Services(SNS) is rapidly increasing with the spread of smartphones. As of 2018, about 2.7 billion people of the world population (about 7.1 billion people) and more than 31.2 million people of the total population of South Korea (about 50.1 million) use SNS. There are several studies have been conducted on increasing SNS market. Most of them, however, were not quantitative but qualitative studies. This study is conducted on domestic SNS market to identify the competitive relationship among SNS platforms with great proportion in South Korea, such as Facebook, Instagram and Twitter. The objective is to suggest some hypotheses of the competitive relations, test them, and finally verify the trend of domestic SNS market. Competitive Lotka-Volterra (LV) model is used to find out the competitive relationships and Moving Window is also used to show the changes of them over time. In order to test the hypotheses on the relationships, some experiments are performed with Moving Window technique. Thus, the relations among the platforms and the changes of them over time are identified.

• Korean Journal of Environmental Agriculture
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• v.32 no.4
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• pp.294-303
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• 2013

BACKGROUND: It is well known that rice-fields can provide excellent foraging places for birds including seasonal migrants, wintering, and breeding and hence the high biodiversity of rice-fields may be expected. However, how environmental change including climate-changes on life-history and population dynamics in birds on rice-fields has not been fully understood. In order to investigate how climate-change affects population migratory patterns and migration timing, I modeled a population dynamics of birds in rice-fields over a whole year. METHODS AND RESULTS: I applied the Lotka-Volterra equation to model the population dynamics of birds that have been foraging/visiting rice-fields in Korea. The simple model involves the number of interspecific individuals and temperature, and the model parameters are periodic in time as the biological activities related to the migration, wintering and reproduction are seasonal. As results, firstly there was a positive relationship between the variation of seasonal population sizes and temperature change. Secondly, the reduced lengths of season were negatively related to the population size. Overall, the effects of the difference of lengths of season on seasonal population dynamics were higher than the effects of seasonal temperature change. CONCLUSION(S): Climate change can alter population dynamics of birds in rice-fields and hence the variation may affect the fitness, such as reproduction, survival and migration. The unstable balances of population dynamics in birds using paddy rice field as affected by climate change can reduce the population growth and species diversity in rice fields. The results suggest that the agricultural production is partly affected by the unstable balance of population in birds using rice-fields.

• 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.

• Korean Journal of Ecology and Environment
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• v.37 no.3 s.108
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• pp.304-312
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• 2004

The transient dynamics of three-trophic populations (prey, predator, and super predator) using ratio-dependent models responding to environmental impacts is analyzed. Environmental factors were divided into two parts: periodic factor (e.g., temperature) and general noise. Periodic factor was addressed as a frequency and bias, while general noise was expressed as a Gaussian distribution. Temperature bias ${\varepsilon}$, temperature frequency ${\Omega}$, and Gaussian noise amplitude ${\`{O}}$ accordingly revealed diverse status of population dynamics in three-trophic food chain, including extinction of species. The model showed stable limit cycles and strange attractors in the long-time behavior depending upon various values of the parameters. The dynamic behavior of the system appeared to be sensitive to changes in environmental input. The parameters of environmental input play an important role in determining extinction time of super predator and predator populations.