• 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 the Korea Society for Simulation
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• v.19 no.3
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• pp.37-43
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• 2010

In field, one can observe without difficulties that two flocks are intersected or combined with each other. For example, a fish flock in a stream separates into two part by obstacles (e.g. stone) and rejoins behind the obstacles. The dynamics of two flocks guided by their leader were studied in the situation where the flocks cross each other with a crossing angle, ${\theta}$, between their moving directions. Each leader is unaffected by its flock members whereas each member is influenced by its leader and other members. To understand the dynamics, I investigated the order parameter, ${\phi}$, defined by the absolute value of the average unit velocity of the flocks' members. When the two flocks were encountered, the first peak in ${\phi}$ was appeared due to the breaking of the flocks' momentum balance. When the flocks began to separate, the second peak in ${\phi}$ was observed. Subsequently, erratic peaks were emerged by some individuals that were delayed to rejoin their flock. The amplitude of the two peaks, $d_1$ (first) and $d_2$ (second), were measured. Interestingly, they exhibited a synchronized behavior for different ${\theta}$. This simulation model can be a useful tool to explore animal behavior and to develop multi-agent robot systems.

• Korean System Dynamics Review
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• v.12 no.2
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• pp.95-126
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• 2011

This paper aims at developing a System Dynamics model with an augmented predator-prey interaction structure to deal with the population management of roe deer in Jeju, Korea. Although people still regard the creature as one of the important tourist attractions, there has been much debate on the issues of the appropriateness of the population size of roe deers because they have been stigmatized as crop damagers, and roadkill/poaching victims due to their natural habit to move around from the top mountain to the lowland of the island. The model is therefore to incorporate these migrating and grazing behaviors into an augmented Lotka-Volterra model coupling roe deer population in both parts of the island to that of predators and preys of the species. The authors also provide a comprehensive set of dynamic hypotheses and relevant CLD/SFD to understand the population dynamics of roe deer and co-evolving species and perform the steady-state analysis of the proposed equation system to verify the model behavior of the numerical example lastly presented in this paper.

• Journal of the Korea Society for Simulation
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• v.20 no.1
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• pp.79-85
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• 2011

The problem of evacuating pedestrians from a room or channel under panic conditions is of obvious importance in daily life. In recent years, several computer models have been developed to simulate pedestrian dynamics. Understanding evacuation dynamics can allow for the design of more comfortable and safe pedestrian facilities. However, these models do not take into account the type and state of mind of pedestrians. They deal with pedestrians as particles and the state of mind as a social force, which is represented by conservative and long-range interactions between individuals. In this study, I used the lattice model proposed in my previous study to explore the evacuation behavior of pedestrians with morality. In this model, three types of pedestrians are considered: adults, children, and injured people. Collisions between adults and children result in injured people. When the number of injured people continuously in contact with each other reaches a given value k, the injured people are removed from the lattice space. This situation is the same as that in which pedestrians start stepping over injured people. This behavior was interpreted as the morality of pedestrians. Simulations showed that the evacuation showed down and eventually became jammed owing to the injured people acting as "obstacles" in relation to the morality k.

• 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.

• Korean Journal of Agricultural and Forest Meteorology
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• v.12 no.2
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• pp.122-131
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• 2010

This paper introduces the concept of a virtual ecosystem and reports the following three mathematical approaches that could be widely used to construct such an ecosystem, along with examples: (1) a molecular dynamics simulation approach for animal flocking behavior, (2) a stochastic lattice model approach for termite colony behavior, and (3) a rule-based cellular automata approach for biofilm growth. The ecosystem considered in this study consists of artificial organisms and their environment. Each organism in the ecosystem is an agent that interacts autonomously with the dynamic environment, including the other organisms within it. The three types of model were successful to account for each corresponding ecosystem. In order to accurately mimic a natural ecosystem, a virtual ecosystem needs to take many ecological variables into account. However, doing so is likely to introduce excess complexity and nonlinearity in the analysis of the virtual ecosystem's dynamics. Nonetheless, the development of a virtual ecosystem is important, because it can provide possible explanations for various phenomena such as environmental disturbances and disasters, and can also give insights into ecological functions from an individual to a community level from a synthetic viewpoint. As an example of how lower and higher levels in an ecosystem can be connected, this paper also briefly discusses the application of the second model to the simulation of a termite ecosystem and the influence of climate change on the termite ecosystem.

• Parasites, Hosts and Diseases
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• v.26 no.4
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• pp.255-262
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• 1988

An epidemiological study on brugian filariasis was carried out in endemic areas including Cheju Island in Korea, with a brief review of literatures. The results showed that the incidence among residents has remarkably decreased in Cheju Island, which was the main endemic area. Reviewing available informations on the prevalence of filariasis reported in recent years and also judging from the present socio·economic conditions which enable people to practice personal protection against mosquitos, it can be said with confidence that alariasis has almost disappeared from Cheju Island and inland areas. The disease is considered to remain at a low level of endemicity in Hugsan Islands. Certainly mass diethylcarbamasine (DEC) treatment carried out in Cheju Island in the 1960s and 1970s and remarkable economic growth followed by improved living standard and altered life-style of inhabitants could all have combined effects on the disappearance of this mosquito-borne disease in this island. If the present trends go on, the possibility of resurgence of filariasis in Cheju Island is hardly postulated.