• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1097-1107
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• 2009

In this paper, three species stage-structured predator-prey model with time delayed and periodic constant impulsive perturbations of predator at fixed times is proposed and investigated. We show that the conditions for the global attractivity of prey(pest)-extinction periodic solution and permanence of the system. Our model exhibits a new modelling method which is applied to investigate impulsive delay differential equations. Our results give some reasonable suggestions for pest management.

• 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.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.311-326
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• 2005

The paper deals with the problem of selective harvesting in a prey-predator model with predator self limitation. Criteria for local stability and global stability for both the exploited and unexploited system are derived. The effort has been considered as a dynamic variable and taxation as a control instrument to protect the fish populations from over exploitation. Finally, the optimal taxation policy is discussed with the help of control theory.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.955-967
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• 2011

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• 한국게임학회 논문지
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• 제13권6호
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• pp.27-34
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• 2013

본 논문은 동물들의 집단행동에서 나타나는 포식자-희생자 관계에서 포식자에 대한 희생자의 추격회피 행동을 분석한다. 희생자가 포식자의 추격을 피하는 하나의 방법이 인접거리에서 급회전을 하는 것이다. 그때 희생자가 추격으로부터 살아남기 위해서는 임계거리와 회전각은 매우 중요하다. 여기서 임계거리는 회전 시작 직전 포식자와 희생자 사이의 거리이다. 이러한 임계거리와 회전각을 분석하기 위하여 본 논문은 추격의 시작에서 보유한 포식자의 에너지와 추격동안 소비한 포식자의 에너지를 이용한다. 시뮬레이션을 통하여, 임계거리가 짧을수록 희생자가 추격으로부터 살아남을 수 있는 회전각은 커진다는 것과 포식자의 질량에 대한 희생자의 질량의 비율이 작아지는 경우에도 역시 회전각 커진다는 것을 알 수 있었다. 시뮬레이션 결과는 자연에서 나타나는 현상과 유사하며, 따라서 이것은 본 논문에서 분석한 방법이 옳다는 것을 의미한다.

• 충청수학회지
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• 제26권4호
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• pp.749-756
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• 2013

In this paper, we consider a diffusive delayed predator-prey model with Beddington-DeAngelis type functional response under homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of immature preys to their maturity. We investigate the global existence of nonnegative solutions and the long-term behavior of the time-dependent solution of the model.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.29-44
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• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.

• 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.

• 대한수학회보
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• 제50권2호
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• pp.353-373
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• 2013

In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.312-326
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• 2021

The prey-predator model is one of the most influential mathematical models in ecology and evolutionary biology. In this study, we considered a modified prey-predator model, which describes the rate of change for each species. The effects of modifications to the classical prey-predator model are investigated here. The conditions required for the existence of the first integral and the stability of the fixed points are studied. In particular, it is shown that the first integral exists only for a subset of the model parameters, and the phase portraits around the fixed points exhibit physically relevant phenomena over a wide range of the parameter space. The results show that adding coupling terms to the classical model widely expands the dynamics with great potential for applicability in real-world phenomena.