• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.433-443
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• 2006

In [1], they build two populations' cellular automata model with predation based on the Penna model. In this paper, uncertain aspects and problems of imprecise and vague data are considered in this model. A fuzzy cellular automata model containing movable wolves and sheep has been built. The results show that the fuzzy cellular automata can simulate the classical CA model and can deal with imprecise and vague data.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.31-56
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• 2007

In this paper, we consider a delay differential equation model of two competing species with harvesting of the mature and immature members of each species. The time delay in the model represents the time from birth to maturity of that species, which appears in the adults recruitment terms. We study the dynamics of our model analytically and we present results on positivity and boundedness of the solution, conditions for the existence and globally asymptotically stable of equilibria, a threshold of harvesting, and the optimal harvesting of the mature populations of each species.

• 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 Academia-Industrial cooperation Society
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• v.12 no.5
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• pp.2067-2077
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• 2011

The recent trend in technology development is characterized as technology convergence, mainly between IT, BT and NT and also more and more industries are starting to use several technologies simultaneously or in a combined way theses days. As a result, the needs on technology interaction analysis is increasing for strategic technology management and policy-making. Responding to the needs, this research deals with technology innovation process in terms of technology competition, particularly focusing on the 17 new growth drivers in 3 areas, which has been announced by the Korean government as a new growth vision for Korean economy, and analyzing their co-evolutionary process. For the analysis, patent data, a representative data on technology innovation, is adopted. Then, Lotka-Volterra Competition model, a model frequently used to describe the dynamism of competitive innovation is applied to the data. The research results are expected to support strategic decision-makings such as effect policy-making or R&D priority-setting, by analyzing the relationship between the 3 areas, the 17 new growth drivers, or the particular technologies in the drivers.

• Informatization Policy
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• v.22 no.2
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• pp.19-34
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• 2015

Due to rapid convergence trends in the digital pay TV market, differentiation among the competing medias decreases and substitutability is increasing. The current study aims to explain the effect of service substitutability among competing media on the size of domestic digital pay TV subscribers. For the analysis, the Lotka-Volterra model, an ecological competitive diffusion model, was used to obtain the basic model for a simulation study. A simulation was performed by adjusting independent variables of substitutability to estimate the size of subscriber for particular media. The relationship between the digital cable TV and the IPTV is identified as a predator-prey relationship and the digital cable TV is found to be superior to the IPTV. The simulation results showed that the increase of convergence and substitutability result in the decrease of the entire media market. Especially, the IPTV is estimated to face the greatest loss in this context.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1411-1427
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• 2009

We propose a model based on Lotka-Volterra dynamics with two competing spices which are affected not only by harvesting but also by the presence of a predator, the third species. Hyperbolic and linear response functions are considered. We derive the conditions for global stability of the system using Lyapunov function. The optimal harvest policy is studied and the solution is derived in the interior equilibrium case using Pontryagin's maximal principle. Finally, some numerical examples are discussed. The nature of variations in the two prey species and one predator species is studied extensively through graphical illustrations.

• 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.

• 사회경제평론
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• no.38
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• pp.51-83
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• 2012

Consider an n goods production economy. Assume the equilibrium condition of Sraffa's price system, a balanced growth condition and the goods market clearing conditions. If both equations are given to determine a real wage rate and investment, the economic system is over-determined. It suggests that there exists no long-period equilibrium to satisfy both labor market and goods market conditions. This paper interprets this situation of over-determinacy as a disequilibrium state, and attempts to solve it through disequilibrium dynamics. It constructs a model of accumulation and real wage rates consistent with Lotka-Volterra system, and shows that the overall growth path fluctuates endogenously around a resting point of long-period disequilibrium.

• 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.