• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1827-1840
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• 2013

This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the nonexistence of non-constant positive steady states, which gives some descriptions of the effect of diffusion on the pattern formation.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.575-587
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• 2006

In this paper, we provide 3 detailed and explicit procedure of obtaining some regions of attraction for the positive steady state (assumed to exist) of a well known Lotka-Volterra type predator-prey system. Also we obtain the sufficient conditions to ensure that the positive equilibrium point of a well known Lotka-Volterra type predator-prey system with a single discrete delay is globally asymptotically stable.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.149-158
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• 2006

In this paper, we consider the Lotka- Volterra predator-prey system, in which constant quantity of the prey is harvested in regular pulses. The ultimate behavior of the solutions starting from different regions is mainly studied. Further, some examples are given to illustrate our results.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.75-87
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• 2018

In this paper, we consider ratio-dependent predator-prey models with disease in the prey under Neumann boundary condition. We investigate sufficient conditions for the existence and non-existence of non-constant positive steady-state solutions by the effects of the induced diffusion rates.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.19-32
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• 2020

We discuss the coexistence of positive solutions to certain strongly-coupled predator-prey elliptic systems under the homogeneous Dirichlet boundary conditions. The sufficient condition for the existence of positive solutions is expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflects the influence of the domain and nonlinearity in the system. Furthermore, applying the obtained results, we investigate the sufficient conditions for the existence of positive solutions of a predator-prey system with degenerate diffusion rates.

• Korean journal of applied entomology
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• v.36 no.3
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• pp.237-242
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• 1997

Comparative studies on suppression possibility with three phytoseiid mite species (An.thly,seiu,sw omersleyi Schicha. A. ,fidIrrc~i.Gs arman and T\ulcornerphlorlrotiiu.s oc~c~idetitaliNs esbit) to the two-spotted spider mite (Te~trrrt~yc.Iir~l~l\ulcorner.i\c .(re Kwh) on kidney bean leaves in field and greenhouse were carried out. In the field experiments with the initial prey -predator ratio of 4 : 1. I0 : I and 20: I . A. ,firllrrcis suppressed successfully the prey populations at all three ratios 17 days after the initial infestation. A. wornc,r-;leyi \uppressed the prey population only at the ratio of 4 : 1, while T. oc~c~ideritcr1iw.s as unable to suppress the prey population at all tested ratios. In the greenhouse experiments with the initial prey-predator ratio of 10: 1, A. jil1ltrci.s could suppress the prey population continuously during the infestation period. A. ~~otnc~r,slceoyuil d suppress the prey population for 13 days after the initial infestation, while T. occie1mttrli.s could suppress the prey population for 8 - 23 days after the initial infestation.

• Journal of Korea Game Society
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• v.13 no.6
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• pp.27-34
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• 2013

This paper analyzes the behaviour of a prey to avoid the pursuit of a predator at predator-prey relationship to be appeared in the collective behavior of animals. One of the methods to avoid the pursuit of a predator is to rotate quickly when a predator arrives near to it. At that moment, a critical distance and a rotating angular are very important for the prey in order to survive from the pursuit, where the critical distance is the distance between the predator and the prey just before rotation. In order to analyze the critical distance and the rotating angular, this paper introduces the energy for a predator which it has at starting point of the chase and consumes during the chase. Through simulations, we can know that the rotating angle for a prey to survive from the pursuit is increased when the critical distance is shorter and when the ratio of predator's mass and prey's mass is also decreased. The results of simulations are the similar phenomenon in nature and therefore it means that the method to analyze in this paper is correct.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.29-44
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• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.27-35
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• 2021

We study the existence of positive T-periodic solutions of ratio-dependent predator-prey systems with time periodic and spatially dependent coefficients. The fixed point theorem by H. Amann is used to obtain necessary and sufficient conditions for the existence of positive T-periodic solutions.