• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.515-527
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• 2008

We investigate a three species food chain system with a Holling type IV functional response and impulsive perturbations. We find conditions for local and global stabilities of prey(or predator) free periodic solutions by applying the Floquet theory and the comparison theorems.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.219-231
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• 2003

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by taking E(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.

• Applied Microscopy
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• v.46 no.2
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• pp.89-92
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• 2016

The bluegill Lepomis macrochirus is an invasive species, not native to Korea, introduced for aquaculture. This species is ranked as a new top predator due to its massive aquatic carnivorous and herbivorous nature by acute vision and the absence of a natural enemy. The visual cells of the retina of L. macrochirus are composed of short single cones and equal double cones and long and bulky rods by light and electron microscopes. In particular, the cones show a regular square mosaic arrangement. This pattern is widely considered as a strong predator. With regard to the visual system, this mosaic pattern may closely be related to a dynamic visual acuity to track and hunt prey.

• 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.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.18 no.2
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• pp.1-17
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• 2015

Ecological reservoir is a multifunctional space where provides the functions of retention, animal habitat and improvement of ecosystem health and landscape. The ecological reservoir of Anteo Eco Park located in Gwangmyeong-si has established to functions for water purification, maintenance of healthy aquatic ecosystem. Because the Anteo Eco Park is located in the site where nonpoint pollutant materials flow in, Anteo Eco Park has potential factors which aquatic ecosystem health deteriorates and damages the habitat of golden frog(Rana plancyi chosenica) which is restoration target species. Therefore, the purpose of this study is to suggest the plan to manage the variables which impede the right functions of aquatic ecosystem by understanding the causal loop diagram for the change of water quality environment and the interaction of predator-prey through system thinking. The results are as follows. First, the study showed that the individual number of golden frog which is an indicator species of Anteo Eco Park is threatened by snakeheaded fish, which is an upper predator. Therefore, balanced food chain should be hold to protect golden frog by capturing the snakeheaded fish which is individual number's density is high, and the monitoring management of the individual number for predator(snakeheaded fish)-prey(golden frog) should be performed. Second, the study represented that water pollution and carnification is caused by the sediment as the dead body of the large emergent vegetation in the winter cumulates as sediment. Ecological reservoir in Anteo Eco Park has been managed by eliminating the dead body of the large emergent vegetation, but the guideline for the proper density maintenance of vegetation community is additionally needed. Lastly, the study showed that aquatic ecosystem of Anteo Eco Park where is contaminated from the inflow of nonpoint pollutants affects the individual number's decline of golden frog and snakeheaded fish. Accordingly, the creation of a buffer area and a substitution wetland is needed in the periphery of the Anteo Eco Park to control the inflow of nonpoint pollutants including organic matters, nutrients and heavy metals. This study will be helpful that Anteo Eco Park improves the regional landscape and maintain healthy aquatic ecosystem space for the park visitors including local residents.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.335-347
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• 2020

In this paper, we take into account a parasite-host system with reaction-diffusion. Firstly, we derive conditions for Hopf, Turing, and wave bifurcations of the system in the spatial domain by means of linear stability and bifurcation analysis. Secondly, we display numerical simulations in order to investigate Turing pattern formation. In fact, the numerical simulation discloses that typical Turing patterns, such as spotted, spot-stripelike mixtures and stripelike patterns, can be formed. In this study, we show that typical Turing patterns, which are well known in predator-prey systems ([7, 18, 25]), can be observed in a parasite-host system as well.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-731
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• 2012

This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.701-717
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• 2006

The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-diffusion is discussed. Especially, when a cross-diffusion is small enough, the existence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross-diffusion is sufficiently large, the extinction of prey species with cross-diffusion interaction to predator occurs. The method employed is the comparison argument for elliptic problem and fixed point theory in a positive cone on a Banach space.

• Journal of the korean society of oceanography
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• v.39 no.4
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• pp.222-233
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• 2004

Using nitrogen as the limiting nutrient, the default version of a microplankton-detritus model linked chlorophyll concentration to the autotroph nitrogen. However, phosphorus dynamics were added to simulate the results of a microcosm experiment. Using standard parameter values with a single value of microheterotroph fraction in the microplankton taken from the observed range, the best simulation successfully captured the main features of the time-courses of chlorophyll and particulate organic carbon, nitrogen and phosphorus, with root-mean-square error equivalent to 29% of particulate concentration. A standard version of microbiological model assumes complete internal cycling of nutrient elements; adding a term for ammonium and phosphate excretion by microheterotrophs did not significantly improve predictions. Relaxing the requirement for constant microheterotroph fraction resulted in an autotroph-heterotroph model AH, with dynamics resembling those of a Lotka-Volterra predator-prey system. AH fitted the microcosm data worse than did MP, justifying the suppression of Lotka-Volterra dynamics in MP. The paper concludes with a discussion of possible reasons for the success of the simple bulk dynamics of MP in simulating microplankton behaviour.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.4 no.3
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• pp.327-336
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• 2004

In distributed autonomous mobile robot system, each robot (predator or prey) must behave by itself according to its states and environments, and if necessary, must cooperate with other robots in order to carry out a given task. Therefore it is essential that each robot have both learning and evolution ability to adapt to dynamic environment. This paper proposes a pursuing system utilizing the artificial life concept where virtual robots emulate social behaviors of animals and insects and realize their group behaviors. Each robot contains sensors to perceive other robots in several directions and decides its behavior based on the information obtained by the sensors. In this paper, a neural network is used for behavior decision controller. The input of the neural network is decided by the existence of other robots and the distance to the other robots. The output determines the directions in which the robot moves. The connection weight values of this neural network are encoded as genes, and the fitness individuals are determined using a genetic algorithm. Here, the fitness values imply how much group behaviors fit adequately to the goal and can express group behaviors. The validity of the system is verified through simulation. Besides, in this paper, we could have observed the robots' emergent behaviors during simulation.