• 생태와환경
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• 제40권2호
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• pp.352-356
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• 2007

The effects of food concentration (Chlorella vulgaris) and predator (Pseudorasbora parva) density on the distributional pattern of Daphnia pulex was evaluated in observation chambers. It was found that in the chamber with higher food concentration, Daphnia began to aggregate and formed tighter swarms. The close distance between each individual and distance from the center of swarm were observed in higher food conditions however, this distributional pattern was not seen in the chamber without food. Thus it suggests that the food is necessary for the swarming behavior of Boptnia in natural habitat. The swarming developed regardless of predator existence and the predator density did not affect swarming pattern of Daphnia.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권2호
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• pp.137-142
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• 2011

In this paper we formulate a predator-prey system in two patches in which the per capita migration rate of each species is influenced only by its own density, i.e. there is no response to the density of the other one. Numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation, i. e. the stable constant steady state loses its stability and spatially non-constant stationary solutions, a pattern emerge.

• 한국시뮬레이션학회논문지
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• 제22권3호
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• pp.1-6
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• 2013

생태계는 다양한 환경 내에 다양한 생물종이 서로 상호작용하고 있는 복잡계이다. 이들 상호작용은 계층적 먹이그물 구조를 이루고 있는데, 많은 경우, 포식자-피식자-식물의 관계를 보여준다. 포식자-피식자 경쟁관계는 시공간적으로 일어나는 현상이기 때문에, 초기시점에서의 개체들 분포와 밀도가 어떠한가는 매우 중요한 정보를 담고 있다. 본 연구에서는, 이들 세 단계 계층구조의 생태계를 간단한 격자 모델로 구성하고 이 모델을 사용하여 각 종의 초기 개체군 밀도가 변함에 따라 생태계 안정성이 어떻게 변하는지를 연구하였다. 격자공간은 $L{\times}L$ 크기의 L(=100) 사각격자로 구성되었다. 식물의 초기 밀도는 0.2로 고정하였다. 시뮬레이션 결과는, 포식자의 밀도가 0.4이하, 피식자의 밀도가 0.5이하일 때 두 종이 공존하는 것을 보여 주었으며, 포식자 밀도가 0.5이상, 피식자 밀도가 0.6 이상의 조건에서는 두 종이 멸종하는 것을 보여 주었다. 공존과 멸종의 두 상태가 접하는 영역의 조건에서는 확률적으로 공존하기도하고 멸종하기도 하는 비선형성이 강한 행동을 보여 주었다. 본 연구를 통해 초기종의 밀도가 생태계 안정성에 매우 중요한 역할을 한다는 것을 알 수 있었다.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.375-406
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• 2020

The anti-predator factor due to fear of predator in eco- epidemiological models has a great importance and cannot be evaded. The present paper consists of a modified Lesli-Gower predator-prey model with contagious disease in the predator population only and also consider the fear effect in the prey population. Boundedness and positivity have been studied to ensure the eco-epidemiological model is well-behaved. The existence and stability conditions of all possible equilibria of the model have been studied thoroughly. Considering the fear constant as bifurcating parameter, the conditions for the existence of limit cycle under which the system admits a Hopf bifurcation are investigated. The detailed study for direction of Hopf bifurcation have been derived with the use of both the normal form and the central manifold theory. We observe that the increasing fear constant, not only reduce the prey density, but also stabilize the system from unstable to stable focus by excluding the existence of periodic solutions.

• Animal cells and systems
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• 제2권2호
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• pp.217-222
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• 1998

Green peach aphid, Myzus persicae(Sulzer) (Homoptera: Aphididae), interacts with many predatory insects in potato fields during the summer. The concept of the predator complex associated with green peach aphids was applied to explain the interactions between the aphid and its predators. The predator power of the predator complex was determined by two factors: the number of predators and the relative feeding capacity. The dynamics of the green peach aphid population was expressed by the number of individuals while the predator power was used to characterize the predator complex. Cumulative degree-days for green peach aphids were used as a time scale to analyze phonology and dynamics patterns of the aphid and its predator complex. The patterns of population changes in aphids were similar during the period of study(1993-1995) although the highest density of aphids fluctuated significantly from year to year. However, the predator power appeared more stable than the green peach aphid population over the three year period. The results indicated that the predator complex plays an important role to suppress the aphid populations during the latter part of the season and that the applications of control measures for green peach aphids in between the initiation and the peak timing of aphid populations are critical to minimize the damage on potatoes.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.329-342
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• 2008

There have been many experimental and observational evidences which indicate the predator response to prey density needs not always monotone increasing as in the classical predator-prey models in population dynamics. Holling type functional response depicts situations in which sufficiently large number of the prey species increases their ability to defend or disguise themselves from the predator. In this paper we investigated the stability and instability property for a Holling type predator-prey system of a generalized form. Hopf type bifurcation properties of the non-diffusive system and the diffusion effects on instability and bifurcation values are studied.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.75-85
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• 2011

In this paper, using the energy estimates and the bootstrap arguments, the global existence of classical solutions for a prey-predator model with non-monotonic functional response and cross-diffusion where the prey and predator both have linear density restriction is proved when the space dimension n < 10.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권3호
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• pp.179-199
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• 2018

The paper explores a tri-trophic food chain model with density dependent mortality of intermediate predator. To analyze this aspect, we have worked out the local stability of different equilibrium points. We have also derived the conditions for global stability of interior equilibrium point and conditions for persistence of model system. To observe the global behaviour of the system, we performed extensive numerical simulations. Our simulation results reveal that chaotic dynamics is produced for increasing value of half-saturation constant. We have also observed trajectory motions around different equilibrium points. It is noticed that chaotic dynamics has been controlled by increasing value of density dependent mortality parameter. So, we conclude that the density dependent mortality parameter can be used to control chaotic dynamics. We also applied basic tools of nonlinear dynamics such as Poincare section and Lyapunov exponent to investigate chaotic behaviour of the system.

• Animal Systematics, Evolution and Diversity
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• 제14권2호
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• pp.159-164
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• 1998

갈거미 속의 일종인 Tetragnatha squamata와 이의 피식자인 차말매미충, Empoasca vitis 사이의 포식 효율에 대하여 실험실 내에서 조사하였다. 피식자의 숫적 증가에 대하여 포식자 거미는 함수적인 반응을 보였다. 포식자가 포식자 자신의 숫적 증가와 포식 효율에 대하여서도 조사하였으며, 이 결과들은 공식으로 표시하였다.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1199-1215
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• 2022

This article aims to study the dynamical behaviours of a two species model in which non-selective harvesting of a prey-predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis is used. A system of two ordinary differential equations(ODE's) has been proposed and analyzed with the predator functional response to prey density is considered as Hassell-Varley type functional responses to study the dynamics of the system. Positivity and boundedness of the system are studied. We have discussed the existence of different equilibrium points and stability of the system at these equilibrium points. We also analysed the system undergoes a Hopf-bifurcation around interior equilibrium point for a various parametric values which has very significant ecological impacts in this work. Computer simulation are carried out to validate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.