• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권3호
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• pp.211-229
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• 2010

Various types of predator-prey systems are studied in terms of the stabilities of their steady-states. Necessary conditions for the existences of non-negative constant steady-states for those systems are obtained. The linearized stabilities of the non-negative constant steady-states for the predator-prey system with monotone response functions are analyzed. The predator-prey system with non-monotone response functions are also investigated for the linearized stabilities of the positive constant steady-states.

• 충청수학회지
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• 제33권1호
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• pp.19-32
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• 2020

We discuss the coexistence of positive solutions to certain strongly-coupled predator-prey elliptic systems under the homogeneous Dirichlet boundary conditions. The sufficient condition for the existence of positive solutions is expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflects the influence of the domain and nonlinearity in the system. Furthermore, applying the obtained results, we investigate the sufficient conditions for the existence of positive solutions of a predator-prey system with degenerate diffusion rates.

• 충청수학회지
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• 제34권1호
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• pp.27-35
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• 2021

We study the existence of positive T-periodic solutions of ratio-dependent predator-prey systems with time periodic and spatially dependent coefficients. The fixed point theorem by H. Amann is used to obtain necessary and sufficient conditions for the existence of positive T-periodic solutions.

• 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.

• 호남수학학술지
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• 제30권3호
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• pp.411-423
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• 2008

In the field of population dynamics and chemical reaction the possibility or the existence of spatially and temporally nonhomogeneous solutions is a very important problem. For last 50 years or so there have been many results on the pattern formation of chemical reaction systems studying reaction systems with or without diffusions to explain instabilities and nonhomogeneous states arising in biological situations. In this paper we study time-dependent properties of a predator-prey system with functional response and give sufficient conditions that guarantee the existence of stable limit cycles.

• 대한수학회논문집
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• 제22권3호
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• pp.465-474
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• 2007

With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system with control. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.

• Animal cells and systems
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• 제3권3호
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• pp.247-252
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• 1999

The aim of this study was to characterize antipredator tactics of anurans and to evaluate the effectiveness of these tactics for predator avoidance in real confrontations. Two types of experiments were conducted. In one experiment, one predator and one prey were placed together for one hour in a small confined space (one-to-one interaction). In another experiment, one predator and several prey were placed together for one day in a large enclosure in a field (field-based interaction). The prey consisted of three anuran species, Rana nigromaculata, R. rugosa, and Bombina orientalls: a snake species, Rhabdophis tigrinus tigrinus, was used as a predator. Results of both experiments demonstrated a range in antipredator responses of the frogs, from toxicity and warning coloration, coupled with slow responses in Bombina to little (or only slight) toxicity, crypsis, and fast take-off responses to the predator in the ranids. oth ranid species exhibited lower survival(57%) than Bombina (95%) in the field-based interaction, suggesting that motor responses of the palatable prey due to attacks of the predator ultimately limited their survival. The jumping of the ranids increased the activity of the predator, which became more likely to strike. Simple crouching(seen in R. rugosa and B. orientalis) and chemical defense (in Bombina) reduced predatory attacks.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.781-802
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• 2011

Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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• pp.225-247
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• 2010

In this paper, we establish a two-competitive-prey and one-predator Holling type II system by introducing a proportional periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for the predator at different fixed time. We show the boundedness of the system and find conditions for the local and global stabilities of two-prey-free periodic solutions by using Floquet theory for the impulsive differential equation, small amplitude perturbation skills and comparison techniques. Also, we prove that the system is permanent under some conditions and give sufficient conditions under which one of the two preys is extinct and the remaining two species are permanent. In addition, we take account of the system with seasonality as a periodic forcing term in the intrinsic growth rate of prey population and then find conditions for the stability of the two-prey-free periodic solutions and for the permanence of this system. We discuss the complex dynamical aspects of these systems via bifurcation diagrams.

• 한국컴퓨터정보학회논문지
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• 제26권9호
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• pp.27-35
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• 2021

인공생명체 연구는 자연 생명과 관련된 시스템이나 그 과정들, 진화 등을 평가해 다양한 응용과학 분야에 활용된다. 이러한 인공생명체의 원활한 활동을 위해 물리적 신체 설계와 행동 제어전략을 진화시키는 연구가 활발히 진행되었다. 그러나 형태와 신경망을 공진화시키는 것은 어렵기에 최적화된 움직임을 가진 인공생명체는 한 가지 형태에 한 가지 움직임만을 가지며 주변 환경 상황은 고려하지 않는 것이 대부분이다. 본 논문에서는 포식자-피식자 모델을 이용하여 형태와 신경망을 공진화하는 인공생명체가 환경적응형 움직임을 갖게 한다. 그런 다음 포식자-피식자 계층 구조를 최상위 포식자-중간 포식자-최하위 피식자 3단계로 확장하여 초기 개체군 밀도에 따라 시뮬레이션의 안정성을 판별하며 형태 진화와 개체군 역학 간의 상관관계를 분석한다.