• Korean Journal of Ecology and Environment
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• v.40 no.2
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• pp.352-356
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• 2007

The effects of food concentration (Chlorella vulgaris) and predator (Pseudorasbora parva) density on the distributional pattern of Daphnia pulex was evaluated in observation chambers. It was found that in the chamber with higher food concentration, Daphnia began to aggregate and formed tighter swarms. The close distance between each individual and distance from the center of swarm were observed in higher food conditions however, this distributional pattern was not seen in the chamber without food. Thus it suggests that the food is necessary for the swarming behavior of Boptnia in natural habitat. The swarming developed regardless of predator existence and the predator density did not affect swarming pattern of Daphnia.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.137-142
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• 2011

In this paper we formulate a predator-prey system in two patches in which the per capita migration rate of each species is influenced only by its own density, i.e. there is no response to the density of the other one. Numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation, i. e. the stable constant steady state loses its stability and spatially non-constant stationary solutions, a pattern emerge.

• Journal of the Korea Society for Simulation
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• v.22 no.3
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• pp.1-6
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• 2013

The ecosystem is the complex system consisting of various biotic and abiotic factors and the factors interact with each other in the hierarchical predator-prey relationship. Since the competitive relation spatiotemporally occurs, the initial state of population density and species distribution are likely to play an important role in the stability of the ecosystem. In the present study, we constructed a lattice model to simulate the three-trophic ecosystem (predatorprey- plant) and using the model, explored how the ecosystem stability is affected by the initial density. The size of lattice space was $L{\times}L$, (L=100) with periodic boundary condition. The initial density of the plant was arbitrarily set as the value of 0.2. The simulation result showed that predator and prey coexist when the density of predator is less than or equal to 0.4 and the density of prey is less than or equal to 0.5. On the other hand, when the predator density is more than or equal to 0.5 and the density of prey is more than or equal to 0.6, both of predator and prey were extinct. In addition, we found that the strong nonlinearity in the interaction between species was observed in the border area between the coexistence and extinction in the species density space.

• 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.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.75-85
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• 2011

In this paper, using the energy estimates and the bootstrap arguments, the global existence of classical solutions for a prey-predator model with non-monotonic functional response and cross-diffusion where the prey and predator both have linear density restriction is proved when the space dimension n < 10.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.179-199
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• 2018

The paper explores a tri-trophic food chain model with density dependent mortality of intermediate predator. To analyze this aspect, we have worked out the local stability of different equilibrium points. We have also derived the conditions for global stability of interior equilibrium point and conditions for persistence of model system. To observe the global behaviour of the system, we performed extensive numerical simulations. Our simulation results reveal that chaotic dynamics is produced for increasing value of half-saturation constant. We have also observed trajectory motions around different equilibrium points. It is noticed that chaotic dynamics has been controlled by increasing value of density dependent mortality parameter. So, we conclude that the density dependent mortality parameter can be used to control chaotic dynamics. We also applied basic tools of nonlinear dynamics such as Poincare section and Lyapunov exponent to investigate chaotic behaviour of the system.

• Animal Systematics, Evolution and Diversity
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• v.14 no.2
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• pp.159-164
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• 1998

The spider, Tetragnatha squamata and its prey Empoasca vitis, the tea leafhopper, were investigated in laboratory on the prey-predator relationship. The predator spider showed a significant response to the increase of the prey. The predation effiency and the response of predator to its density were examined as well. The result of the experiments are give as questions.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1199-1215
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• 2022

This article aims to study the dynamical behaviours of a two species model in which non-selective harvesting of a prey-predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis is used. A system of two ordinary differential equations(ODE's) has been proposed and analyzed with the predator functional response to prey density is considered as Hassell-Varley type functional responses to study the dynamics of the system. Positivity and boundedness of the system are studied. We have discussed the existence of different equilibrium points and stability of the system at these equilibrium points. We also analysed the system undergoes a Hopf-bifurcation around interior equilibrium point for a various parametric values which has very significant ecological impacts in this work. Computer simulation are carried out to validate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.