• 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.

• Animal cells and systems
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• v.2 no.2
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• pp.217-222
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• 1998

Green peach aphid, Myzus persicae(Sulzer) (Homoptera: Aphididae), interacts with many predatory insects in potato fields during the summer. The concept of the predator complex associated with green peach aphids was applied to explain the interactions between the aphid and its predators. The predator power of the predator complex was determined by two factors: the number of predators and the relative feeding capacity. The dynamics of the green peach aphid population was expressed by the number of individuals while the predator power was used to characterize the predator complex. Cumulative degree-days for green peach aphids were used as a time scale to analyze phonology and dynamics patterns of the aphid and its predator complex. The patterns of population changes in aphids were similar during the period of study(1993-1995) although the highest density of aphids fluctuated significantly from year to year. However, the predator power appeared more stable than the green peach aphid population over the three year period. The results indicated that the predator complex plays an important role to suppress the aphid populations during the latter part of the season and that the applications of control measures for green peach aphids in between the initiation and the peak timing of aphid populations are critical to minimize the damage on potatoes.

• 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.

• The Pure and Applied Mathematics
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• v.17 no.3
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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.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.311-326
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• 2005

The paper deals with the problem of selective harvesting in a prey-predator model with predator self limitation. Criteria for local stability and global stability for both the exploited and unexploited system are derived. The effort has been considered as a dynamic variable and taxation as a control instrument to protect the fish populations from over exploitation. Finally, the optimal taxation policy is discussed with the help of control theory.

• 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 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.

• The Pure and Applied Mathematics
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• v.15 no.3
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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.

• Animal cells and systems
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• v.3 no.3
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• pp.247-252
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• 1999

The aim of this study was to characterize antipredator tactics of anurans and to evaluate the effectiveness of these tactics for predator avoidance in real confrontations. Two types of experiments were conducted. In one experiment, one predator and one prey were placed together for one hour in a small confined space (one-to-one interaction). In another experiment, one predator and several prey were placed together for one day in a large enclosure in a field (field-based interaction). The prey consisted of three anuran species, Rana nigromaculata, R. rugosa, and Bombina orientalls: a snake species, Rhabdophis tigrinus tigrinus, was used as a predator. Results of both experiments demonstrated a range in antipredator responses of the frogs, from toxicity and warning coloration, coupled with slow responses in Bombina to little (or only slight) toxicity, crypsis, and fast take-off responses to the predator in the ranids. oth ranid species exhibited lower survival(57%) than Bombina (95%) in the field-based interaction, suggesting that motor responses of the palatable prey due to attacks of the predator ultimately limited their survival. The jumping of the ranids increased the activity of the predator, which became more likely to strike. Simple crouching(seen in R. rugosa and B. orientalis) and chemical defense (in Bombina) reduced predatory attacks.

• 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.