• 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.

• 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.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.193-207
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• 2010

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

• 대한수학회지
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• 제44권2호
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• pp.327-342
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• 2007

In this paper, a kind of pest-predator model with impulsive effect and infinite delay is considered by the method of chain transform. By using Floquet's theorem, it is shown that there exists a globally asymptotically stable periodic pest eradication solution when the impulsive period is less than or equal to some critical value which is a directly proportional function with respect to the population of release. Furthermore, it is proved that the system is permanent if the impulsive period is larger than some critical value. Finally, the results of the corresponding systems are compared, those results obtained in this paper are confirmed by numerical simulation.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.503-514
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• 2008

We investigate a three-species food chain system with Lotka-Volterra functional response and impulsive perturbations. In [23], Zhang and Chen have studied the system. They have given conditions for extinction of lowest-level prey and top predator and considered the local stability of lower-level prey and top predator eradication periodic solution. However, they did not give a condition for permanence, which is one of important facts in population dynamics. In this paper, we establish the condition for permanence of the three-species food chain system with impulsive perturbations. In addition, we give some numerical examples.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.721-741
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• 2011

In this paper we have considered a dynamical mathematical model of the sub-populations of potential smokers (non-smokers), smokers, smokers who temporarily quit smoking, smokers who permanently quit smoking and a class of smoking associated illness by introducing time dependent parameters and distributed time delay to acquire smoking habit. Here, we have established some sufficient conditions on the permanence and extinction of the smoking class in the community by using inequality analytical technique. We have introduced some new threshold values $R_0$ and $R^*$ and further obtained that the smoking class in the community will be permanent when $R_0$ > 1 and the smoking class in the community will be going to extinct when $R^*$ < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. 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.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• 지적과 국토정보
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• 제48권2호
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• pp.65-77
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• 2018

빈집 연구에 있어 발생 영향 요인 파악은 매우 중요하다. 연구의 목적은 농촌 지역의 빈집 발생에 영향을 주는 요인을 분석하는 것이다. 121개 연구 대상 지역을 설정하고, 8개의 독립변수(노후 주택 비율, 주택 거래 비율, 주택 보급률, 지역 소멸 지수, 순 이동률, 지역 노령화 지수, 인구 대비 종사자수, 재정자립도)와 1개 종속변수(빈집 비율)를 선정하였다. 연구 결과, 첫째, 일반농산어촌 지역 전체를 대상으로 하는 모형 1과 군 지역을 대상으로 하는 모형 2는 모두 통계적으로 유의미하였으며, 잔차의 독립성에 문제가 없었다. 둘째, 지역 소멸 지수 및 노후 주택 비율의 경우 모형 1과 모형 2에서 모두 통계적으로 유의미한 정(+)의 관계가 있는 것으로 분석되었으며, 셋째, 주택 보급률의 경우, 모형 1에서만 통계적으로 유의미한 정(+)의 관계가 있는 것으로 분석되었고, 주택 거래 비율의 경우, 모형 2에서 통계적으로 유의미한 반(-)의 관계가 있는 것으로 분석되었다. 연구의 시사점가 도출되었다. 첫째, 가구 및 인구 증가가 없는 주택 보급률의 상승은 지역 내 빈집의 발생 확률을 높이는 것을 시사하고, 노후 주택 비율이 높을수록 빈집 발생 확률이 높아진다. 둘째, 주택 거래 활성화를 위해서는 지역의 중장기 발전을 위한 투자 유입이 필요하다. 셋째, 지역 소멸 지수는 빈집 비율과 유의미한 관계를 가지므로, 지역의 영속성을 위해 장기적인 시각에서 지역 활성화 정책이 도입되어야 한다.