• 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 applied mathematics & informatics
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• v.40 no.3_4
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• pp.393-407
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• 2022

In this paper, a diffusive predator-prey system with Beddington DeAngelis functional response and the modified Leslie-Gower type predator dynamics when a prey population is infected is considered. The predator is assumed to predate both the susceptible prey and infected prey following the Beddington-DeAngelis functional response and Holling type II functional response, respectively. The predator follows the modified Leslie-Gower predator dynamics. Both the prey, susceptible and infected, and predator are assumed to be distributed in-homogeneous in space. A reaction-diffusion equation with Neumann boundary conditions is considered to capture the dynamics of the prey and predator population. The global attractor and persistence properties of the system are studied. The priori estimates of the non-constant positive steady state of the system are obtained. The existence of non-constant positive steady state of the system is investigated by the use of Leray-Schauder Theorem. The existence of non-constant positive steady state of the system, with large diffusivity, guarantees for the occurrence of interesting Turing patterns.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.375-406
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• 2020

The anti-predator factor due to fear of predator in eco- epidemiological models has a great importance and cannot be evaded. The present paper consists of a modified Lesli-Gower predator-prey model with contagious disease in the predator population only and also consider the fear effect in the prey population. Boundedness and positivity have been studied to ensure the eco-epidemiological model is well-behaved. The existence and stability conditions of all possible equilibria of the model have been studied thoroughly. Considering the fear constant as bifurcating parameter, the conditions for the existence of limit cycle under which the system admits a Hopf bifurcation are investigated. The detailed study for direction of Hopf bifurcation have been derived with the use of both the normal form and the central manifold theory. We observe that the increasing fear constant, not only reduce the prey density, but also stabilize the system from unstable to stable focus by excluding the existence of periodic solutions.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.361-377
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• 2005

A mathematical model dealing with a prey-predator system with disease in the prey is considered. The functional response of the predator is governed by a Hoilling type-2 function. Mathematical analysis of the model regarding stability and persistence has been performed. The effect of delay and diffusion on the above system is studied. The role of diffusivity on stability and persistence criteria of the system has also been discussed.

• Journal of Korea Game Society
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• v.13 no.1
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• pp.41-48
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• 2013

In general, the predator-prey model has been studied as a model of struggle for existence in a ecosystem. While conventional papers have focussed on the population change of the predator-prey, this paper focused on controlling the energy needed for the predator to pursue the prey. For simplification, assume the environment which there are only single predator and prey. Based on the environment, a certain amount of energy needed for a predator to pursue the prey was suggested on a basis of physical theories and also the used energy model was suggested on a basis of the simulation. From experiments, it was proven that the suggested energy models were appropriate for natural pursuit.

• 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 Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.312-326
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• 2021

The prey-predator model is one of the most influential mathematical models in ecology and evolutionary biology. In this study, we considered a modified prey-predator model, which describes the rate of change for each species. The effects of modifications to the classical prey-predator model are investigated here. The conditions required for the existence of the first integral and the stability of the fixed points are studied. In particular, it is shown that the first integral exists only for a subset of the model parameters, and the phase portraits around the fixed points exhibit physically relevant phenomena over a wide range of the parameter space. The results show that adding coupling terms to the classical model widely expands the dynamics with great potential for applicability in real-world phenomena.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.749-756
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• 2013

In this paper, we consider a diffusive delayed predator-prey model with Beddington-DeAngelis type functional response under homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of immature preys to their maturity. We investigate the global existence of nonnegative solutions and the long-term behavior of the time-dependent solution of the model.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.955-967
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• 2011

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. 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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• 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.