• 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.55 no.4
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• pp.259-273
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• 2022

Interactions between species in a community are very complex, and they are visualized and analyzed through a food web in simple way. Food web is a network of species connected by trophic links showing energy flow from prey to predator. Various models were developed to characterize the food web in ecosystems. In this study, we classified food web models to static models such as Ecopath and dynamic models such as AQUATOX. We presented characteristics of several different types of food web models in each category, and reviewed their applications used in aquatic ecosystems. Finally, we presented issues to be considered to develop food web models.

• Journal of the Korea Society for Simulation
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• v.22 no.3
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• pp.1-6
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• 2013

The ecosystem is the complex system consisting of various biotic and abiotic factors and the factors interact with each other in the hierarchical predator-prey relationship. Since the competitive relation spatiotemporally occurs, the initial state of population density and species distribution are likely to play an important role in the stability of the ecosystem. In the present study, we constructed a lattice model to simulate the three-trophic ecosystem (predatorprey- plant) and using the model, explored how the ecosystem stability is affected by the initial density. The size of lattice space was $L{\times}L$, (L=100) with periodic boundary condition. The initial density of the plant was arbitrarily set as the value of 0.2. The simulation result showed that predator and prey coexist when the density of predator is less than or equal to 0.4 and the density of prey is less than or equal to 0.5. On the other hand, when the predator density is more than or equal to 0.5 and the density of prey is more than or equal to 0.6, both of predator and prey were extinct. In addition, we found that the strong nonlinearity in the interaction between species was observed in the border area between the coexistence and extinction in the species density space.