• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.1
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• pp.86-93
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• 2012

This paper presents a new approach to solve the pursuit problem based on a univector field method. In our proposed method, a set of eight agents works together instantaneously to find suitable moving directions and follow the univector field to pursue and capture a prey agent by surrounding it from eight directions in an infinite grid-world. In addition, a set of strategies is proposed to make the pursuit problem more realistic in the real world environment. This is a general approach, and it can be extended for an environment that contains static or moving obstacles. Experimental results show that our proposed algorithm is effective for the pursuit problem.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.677-690
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• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• 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.