• Journal of applied mathematics & informatics
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• 제40권3_4호
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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.

• ALGAE
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• 제30권1호
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• pp.35-47
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• 2015

The marine sand-dwelling dinoflagellate Polykrikos lebourae possesses obvious gold-brown pigmented plastids as well as taeniocyst-nematocyst complex structures. Despite of the presence of the visible plastids, previous attempts to establish this species in culture all failed and thus the unavailability of cultures of this species has posed a major obstacle to further detailed exploration of ecophysiology of the dinoflagellate. Here, we isolated P. lebourae from sandy sediment of an intertidal flat on Korean western coast, successfully established it in culture, and have been maintaining the stock culture over the past 3 years. Using this stock culture, we explored phagotrophy and potential prey resources of P. lebourae, growth and grazing responses of P. lebourae to different prey organisms, the effect of prey concentration on growth and grazing rates and gross growth efficiency (GGE) of P. lebourae when fed three different prey organisms, and the growth kinetics of P. lebourae under different light regimes. P. lebourae captured prey cells using a tow filament and then phagocytized them through the posterior end. The dinoflagellate was capable of ingesting a broad range of prey species varying in size, but not all prey species tested in this study supported its sustained growth. GGE of P. lebourae was extremely high at low prey concentration and moderate or low at high prey concentrations, indicating that P. lebourae grows heterotrophically at high prey concentrations but its growth seems to be more dependent on a certain growth factor or photosynthesis of plastids derived from the prey. In the presence of prey in excess, P. lebourae grew well at moderate light intensity of $40{\mu}mol$ photons $m^{-2}s^{-1}$, but did not grow at dim and high (10 or $120{\mu}mol$ photons $m^{-2}s^{-1}$) light intensities. Our results suggest that the benthic dinoflagellate P. lebourae is an obligate mixotroph, requiring both prey and light for sustained growth and survival.

• ALGAE
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• 제31권1호
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• pp.17-31
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• 2016

To explore the feeding ecology of the newly described heterotrophic dinoflagellate Aduncodinium glandula in the family Pfiesteriaceae, its feeding behavior and prey species were investigated. Additionally, the growth and ingestion rates of A. glandula on the mixotrophic dinoflagellates Heterocapsa triquetra and Akashiwo sanguinea, its optimal and suboptimal prey, respectively were measured. A. glandula fed on prey through a peduncle after anchoring to the prey using a tow filament. A. glandula ate all algal prey and perch blood cells tested and had the most diverse prey species in the family Pfiesteriaceae. Unlike for other pfiesteriacean species, H. triquetra and A. sanguinea support the positive growth of A. glandula. However, the cryptophytes Rhodomonas salina and Teleaulax sp. and the phototrophic dinoflagellate Amphidinium carterae did not support the positive growth of A. glandula. Thus, A. glandula may have a unique kind of prey and its optimal prey differs from that of the other pfiesteriacean dinoflagellates. With increasing mean prey concentration, the growth rates of A. glandula on H. triquetra and A. sanguinea increased rapidly and then slowed or became saturated. The maximum growth rates when feeding on H. triquetra and A. sanguinea were 1.004 and 0.567 d⁻¹, respectively. Further, the maximum ingestion rates of A. glandula on H. triquetra and A. sanguinea were 0.75 and 1.38 ng C predator⁻¹ d⁻¹, respectively. There is no other pfiesteriacean species having H. triquetra and A. sanguinea as optimal and suboptimal prey. Thus, A. glandula may be abundant during blooms dominated by these species not preferred by the other pfiesteriacean dinoflagellates.

• ALGAE
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• 제32권1호
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• pp.67-74
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• 2017

The heterotrophic dinoflagellate Oxyrrhis marina is known to produce high levels of docosahexaenoic acid (DHA) when fed on diverse algal prey. However, large-scale culturing of algal prey species is not easy and requires a large amount of budget, and thus more easily cultivable and low-cost prey is required. Dried yeast was selected as a strong candidate for an alternative prey in our preliminary tests. Thus, we explored the fatty acid composition and DHA production of O. marina fed on dried yeast and compared these results to those of O. marina fed on two algal prey species: the phototrophic dinoflagellate Amphidinium carterae and chlorophyte Chlorella sp. powder. O. marina fed on dried yeast, which does not contain DHA, produced the same high level of DHA as those fed on DHA-containing A. carterae. This indicates that O. marina is likely to produce DHA by itself regardless of prey items. Furthermore, the DHA content (and portion of total fatty acid methyl esters) of O. marina satiated with dried yeast, 52.40 pg per cell(and 25.9%), was considerably greater than that of O. marina fed on A. carterae (26.91 pg per cell; 15.7%) or powder of Chlorella sp. powder (21.24 pg per cell; 16.7%). The cost of dried yeast (approximately 10 US dollars for 1 kg dried yeast) was much lower than that of obtaining the algal prey (approximately 160 US dollars for 1 kg A. carterae). Therefore, compared to conventional algal prey, dried yeast is a more easily obtainable and lower-cost prey for use in the production of DHA by O. marina.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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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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• 제17권1_2_3호
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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.

• 충청수학회지
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• 제26권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권3호
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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.

• Kyungpook Mathematical Journal
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• 제49권4호
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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.

• 호남수학학술지
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• 제30권3호
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• pp.521-533
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• 2008

We investigate a periodically forced Lotka-Volterra type predator-prey system with impulsive perturbations - seasonal effects on the prey, periodic releasing of natural enemies(predator) and spraying pesticide at the same fixed times. We show that the solutions of the system are bounded using the comparison theorems and find conditions for the stability of a stable prey-free solution and for the permanence of the system.