• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.515-527
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• 2008

We investigate a three species food chain system with a Holling type IV functional response and impulsive perturbations. We find conditions for local and global stabilities of prey(or predator) free periodic solutions by applying the Floquet theory and the comparison theorems.

• 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.

• 대한수학회지
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• 제55권1호
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• pp.43-58
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• 2018

In this paper, we study a delayed predator-prey system with Holling type IV functional response incorporating the effect of habitat complexity. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. The explicit formulas which determine the direction and stability of Hopf bifurcation are obtained by the normal form theory and the center manifold theorem.

• 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.