• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.647-660
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• 2013

In the paper, a two-prey one-predator system with defensive ability and Holling type-II functional responses is investigated. First, the stability of equilibrium points of the system is discussed and then conditions for the persistence of the system are established according to the existence of limit cycles. Numerical examples are illustrated to attest to our mathematical results. Finally, via bifurcation diagrams, various dynamic behaviors including chaotic phenomena are demonstrated.

• 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 the Korean Society for Industrial and Applied Mathematics
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• 제16권3호
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• pp.151-167
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• 2012

In this paper, we investigate the dynamic behaviors of a one-prey and two-predator system with Holling-type II functional response and defensive ability by introducing a proportion that is periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for predators at different fixed time. We establish conditions for the local stability and global asymptotic stability of prey-free periodic solutions by using Floquet theory for the impulsive equation, small amplitude perturbation skills. Also, we prove that the system is uniformly bounded and is permanent under some conditions via comparison techniques. By displaying bifurcation diagrams, we show that the system has complex dynamical aspects.

• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.211-217
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• 2009

In this paper, we are studying the property for permanence of a three species food chain system with impulsive perturbations and Holling type II functional response, species which is important concept or property in ecological systems. Specially, we give the conditions for the permanence of this system. To do it, we consider the comparison method which is typical skill happened in impulsive differential inequalities. In addition, we reaffirm our results by using a numerical example.

• 대한수학회논문집
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• 제23권2호
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• pp.211-227
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• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• 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.

• 한국응용곤충학회지
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• 제34권3호
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• pp.234-242
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• 1995

멸구류 포식성 천적인 등검은황록장님노린재의 온도에 따른 벼멸구 알 공격능력과 기능반응의 변화를 20, 23, 26, 29, 32, $35^{\circ}C$ 등 6개 온도에서 검정하였다. 등검은 황록장님노린재는 산란된지 1일에서 4일된 이런시기의 벼멸구 알을 선호하였으며, 이중 3일된 벼멸구 알을 가장 선호하였다. 등검은황록장님노린재의 벼멸구 알에 대한 포식능력은 Holling의 제2형 기능반응의 Rogers(1972) 진정포식자 모형에 잘 부합되었다. 기능반응의 포식자 탐색율(a)은 $32^{\circ}C$까지는 온도가 높아짐에 따라 증가하는 경향이었으나 $35^{\circ}C$에서는 급격히 감소하였다. 그러나 처리시간(Th)은 온도가 높아짐에 따라 완만히 감소되었다. 등검은황록장님노린재의 벼멸구 알에 대한 온도별, 밀도별 공격위치의 선호성은 일반적으로 저밀도에서는 큰 차이가 없었으나 고밀도에서는 위쪽에 산란된 알을 더 선호하는 경향이었으며 특히 온도가 높아짐에따라 이러한 경향이 더욱 뚜렷이 나타났다.