• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.393-407
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• 2022

In this paper, a diffusive predator-prey system with Beddington DeAngelis functional response and the modified Leslie-Gower type predator dynamics when a prey population is infected is considered. The predator is assumed to predate both the susceptible prey and infected prey following the Beddington-DeAngelis functional response and Holling type II functional response, respectively. The predator follows the modified Leslie-Gower predator dynamics. Both the prey, susceptible and infected, and predator are assumed to be distributed in-homogeneous in space. A reaction-diffusion equation with Neumann boundary conditions is considered to capture the dynamics of the prey and predator population. The global attractor and persistence properties of the system are studied. The priori estimates of the non-constant positive steady state of the system are obtained. The existence of non-constant positive steady state of the system is investigated by the use of Leray-Schauder Theorem. The existence of non-constant positive steady state of the system, with large diffusivity, guarantees for the occurrence of interesting Turing patterns.

• 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.

• 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.

• 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.

• 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.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.763-770
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• 2009

We investigate the dynamical properties of a Holling type I predator-prey model, which harvests both prey and predator and stock predator impulsively. By using the Floquet theory and small amplitude perturbation method we prove that there exists a stable prey-extermination solution when the impulsive period is less than some critical value, which implies that the model could be extinct under some conditions. Moreover, we give a sufficient condition for the permanence of the model.

• 한국게임학회 논문지
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• 제13권1호
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• pp.41-48
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• 2013

일반적으로 생태계에서 포식자-희생자 모델은 생존 경쟁의 연구모델로서 많이 연구되어 왔다. 기존의 논문이 포식자-희생자의 개체 수 변화량에 초점을 맞추고 있는 반면, 본 논문은 포식자-희생자 모델에서 포식자가 희생자를 추격하기에 필요한 에너지 제어에 관한 연구를 하였다. 문제를 간단히 하기 위하여 한 마리의 포식자와 한 마리의 희생자가 있다고 가정하였고, 이를 기반으로 일정한 거리에 있는 포식자가 희생자를 추격하여 성공하기에 필요 에너지를 물리적 이론을 근거로 제시하였고, 시뮬레이션에 기반하여 소비 에너지 모델을 제안하였다. 실험을 통하여 제안된 두 에너지 모델이 자연스러운 추격하기에 올바르게 적용될 수 있음을 보였다.

• 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.

• 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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• 제17권1_2_3호
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• pp.361-377
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• 2005

A mathematical model dealing with a prey-predator system with disease in the prey is considered. The functional response of the predator is governed by a Hoilling type-2 function. Mathematical analysis of the model regarding stability and persistence has been performed. The effect of delay and diffusion on the above system is studied. The role of diffusivity on stability and persistence criteria of the system has also been discussed.