• Journal of applied mathematics & informatics
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• v.27 no.5_6
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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.

• Kyungpook Mathematical Journal
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• v.49 no.4
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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 the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.225-247
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• 2010

In this paper, we establish a two-competitive-prey and one-predator Holling type II system by introducing a proportional periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for the predator at different fixed time. We show the boundedness of the system and find conditions for the local and global stabilities of two-prey-free periodic solutions by using Floquet theory for the impulsive differential equation, small amplitude perturbation skills and comparison techniques. Also, we prove that the system is permanent under some conditions and give sufficient conditions under which one of the two preys is extinct and the remaining two species are permanent. In addition, we take account of the system with seasonality as a periodic forcing term in the intrinsic growth rate of prey population and then find conditions for the stability of the two-prey-free periodic solutions and for the permanence of this system. We discuss the complex dynamical aspects of these systems via bifurcation diagrams.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.3
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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 Institute of Telematics and Electronics B
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• v.28B no.5
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• pp.335-342
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• 1991

A real-tme nonlinear parameter tomography is pumping wave method. This tomorgraphy has a merit which requires no 180$^{\circ}$ projection datum, while the ray-bending effect is remrkably remained on the reconstructed image. In this paper we intend to compensate this ray-bending effect using the perturbation method. Impulsive pumping wave makes derived compensative term simple form, nad the compensative image is easily obtained. We perform computer simulation to confirm the improvement of corrected imate.

• Bulletin of the Korean Space Science Society
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• 2008.10a
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• pp.23.3-23.3
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• 2008

In this study, the nature of nonlinear field line resonances (FLR) is studied by adopting full MHD simulations. The MHD code used here is based on the total variation diminishing (TVD) scheme and we have performed numerical simulations of FLR with its three-dimensional code. If the source perturbation is strongly impulsive and thus the timescale of the initial variations is sufficiently smaller than the convection timescale, FLRs are easily confirmed in these simulations. When the disturbance is sufficiently small, it is shown that linear properties of MHD wave coupling are well reproduced. In order to examine nonlinear nature of FLR, wave spectra, Poynting flux and energy distribution are studied at resonances as the magnitude of initial disturbance gradually increases.