• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.35-50
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• 2007

In this work, optimal harvesting policy for the predator-prey system of three species with age-dependent and diffusion is discussed. Existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.139-151
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• 2008

We investigate a three species food chain system with Lotka-Volterra type functional response and impulsive perturbations. We find a condition for the local stability of prey or predator free periodic solutions by applying the Floquet theory and the comparison theorems and show the boundedness of this system. Furthermore, we illustrate some examples.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.515-527
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• 2008

We investigate a three species food chain system with a Holling type IV functional response and impulsive perturbations. We find conditions for local and global stabilities of prey(or predator) free periodic solutions by applying the Floquet theory and the comparison theorems.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.231-243
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• 2007

In this paper, we study a Lotka-Volterra type simple food chain model. We investigate the positive coexistence of the steady states to the model and give some results for the extinction of species under certain assumptions which can be interpreted as Domino effect and Biological control. The methods of a decoupling operator and the fixed point index theory on a positive cone are used as well as the comparison argument. Numerical evidences for our results also are provided.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.93-102
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• 2004

A model of three trophic level food chain with ratio dependence is considered. The existencem uniqueness and stability of its solutions are investigated.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.273-286
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• 2005

Parameter identification problem of a three species (predator, mutualist-prey, and mutualist) ecological system with reaction-diffusion phenomenon is investigated in this paper. The mathematical model of the parameter identification problem is constructed and continuous dependence of the solution for the direct problem on the parameters identified is obtained. Finally, the existence of optimal solution and an optimality necessary condition for the parameter identification problem are given.

• ALGAE
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• v.36 no.4
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• pp.263-283
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• 2021

To explore the ecophysiological characteristics of the kleptoplastidic dinoflagellate Shimiella gracilenta, we determined its spatiotemporal distribution in Korean coastal waters and growth and ingestion rates as a function of prey concentration. The abundance of S. gracilenta at 28 stations from 2015 to 2018 was measured using quantitative real-time polymerase chain reaction. Cells of S. gracilenta were detected at least once at all the stations and in each season, when temperature and salinity were 1.7-26.4℃ and 9.9-35.6, respectively. Moreover, among the 28 potential prey species tested, S. gracilenta SGJH1904 fed on diverse prey taxa. However, the highest abundance of S. gracilenta was only 3 cells mL^-1 during the study period. The threshold Teleaulax amphioxeia concentration for S. gracilenta growth was 5,618 cells mL^-1, which was much higher than the highest abundance of T. amphioxeia (667 cells mL^-1). Thus, T. amphioxeia was not likely to support the growth of S. gracilenta in the field during the study period. However, the maximum specific growth and ingestion rates of S. gracilenta on T. amphioxeia, the optimal prey species, were 1.36 d^-1 and 0.04 ng C predator^-1 d^-1, respectively. Thus, if the abundance of T. amphioxeia was much higher than 5,618 cells mL^-1, the abundance of S. gracilenta could be much higher than the highest abundance observed in this study. Eurythermal and euryhaline characteristics of S. gracilenta and its ability to feed on diverse prey species and conduct kleptoplastidy are likely to be responsible for its common spatiotemporal distribution.

• ALGAE
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• v.29 no.2
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• pp.137-152
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• 2014

Mixotrophic protists play diverse roles in marine food webs as predators and prey. Thus, exploring mixotrophy in phototrophic protists has emerged as a critical step in understanding marine food webs and cycling of materials in marine ecosystem. To investigate the feeding of newly described mixotrophic dinoflagellate Ansanella granifera, we explored the feeding mechanism and the different types of species that A. granifera was able to feed on. In addition, we measured the growth and ingestion rates of A. granifera feeding on the prasinophyte Pyramimonas sp., the only algal prey, as a function of prey concentration. A. granifera was able to feed on heterotrophic bacteria and the cyanobacterium Synechococcus sp. However, among the 12 species of algal prey offered, A. granifera ingested only Pyramimonas sp. A. granifera ingested the algal prey cell by engulfment. With increasing mean prey concentration, the growth rate of A. granifera feeding on Pyramimonas sp. increased rapidly, but became saturated at a concentration of $434ngCmL^{-1}$ (10,845 cells $mL^{-1}$). The maximum specific growth rate (i.e., mixotrophic growth) of A. granifera feeding on Pyramimonas sp. was $1.426d^{-1}$, at $20^{\circ}C$ under a 14 : 10 h light-dark cycle of $20{\mu}Em^{-2}s^{-1}$, while the growth rate (i.e., phototrophic growth) under similar light conditions without added prey was $0.391d^{-1}$. With increasing mean prey concentration, the ingestion rate of A. granifera feeding on Pyramimonas sp. increased rapidly, but slightly at the concentrations ${\geq}306ngCmL^{-1}$ (7,649 cells $mL^{-1}$). The maximum ingestion rate of A. granifera feeding on Pyramimonas sp. was 0.97 ng C $predator^{-1}d^{-1}$ (24.3 cells $grazer^{-1}d^{-1}$). The calculated grazing coefficients for A. granifera feeding on co-occurring Pyramimonas sp. were up to $2.78d^{-1}$. The results of the present study suggest that A. granifera can sometimes have a considerable grazing impact on the population of Pyramimonas spp.

• Korean Journal of Ecology and Environment
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• v.37 no.3 s.108
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• pp.304-312
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• 2004

The transient dynamics of three-trophic populations (prey, predator, and super predator) using ratio-dependent models responding to environmental impacts is analyzed. Environmental factors were divided into two parts: periodic factor (e.g., temperature) and general noise. Periodic factor was addressed as a frequency and bias, while general noise was expressed as a Gaussian distribution. Temperature bias ${\varepsilon}$, temperature frequency ${\Omega}$, and Gaussian noise amplitude ${\`{O}}$ accordingly revealed diverse status of population dynamics in three-trophic food chain, including extinction of species. The model showed stable limit cycles and strange attractors in the long-time behavior depending upon various values of the parameters. The dynamic behavior of the system appeared to be sensitive to changes in environmental input. The parameters of environmental input play an important role in determining extinction time of super predator and predator populations.

• Korean Journal of Ichthyology
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• v.26 no.4
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• pp.303-309
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• 2014

Feeding ecology of Collichthys lucidus was determined by analysis of stomach contents of 926 specimens ranged from 3.5 to 18.5 cm in the Han River estuary. This fish actively fed on benthic crustaceans, mainly decapods, Palaemon carinicauda and Acetes chinensis, and they can be defined as the benthivorous predator. The percentage of empty stomachs was 23.8%. The vacuity index (VI) did not vary with the size classes, but showed significant monthly variations. Monthly variation of feeding activity appears to be related to the reproduction cycle of the fish, and to the temporal abundance of the prey organisms. Collichthys lucidus in Han River estuary fed on a wide array of prey items and could be considered as a non-selective predator.