• 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.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1379-1393
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• 2010

In this paper, a stage-structured predator prey model (stage structure on prey) with two discrete time delays has been discussed. The two discrete time delays occur due to maturation delay and gestation delay. Linear stability analysis for both non-delay as well as with delays reveals that certain thresholds have to be maintained for coexistence. Numerical simulation shows that the system exhibits Hopf bifurcation, resulting in a stable limit cycle.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1097-1107
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• 2009

In this paper, three species stage-structured predator-prey model with time delayed and periodic constant impulsive perturbations of predator at fixed times is proposed and investigated. We show that the conditions for the global attractivity of prey(pest)-extinction periodic solution and permanence of the system. Our model exhibits a new modelling method which is applied to investigate impulsive delay differential equations. Our results give some reasonable suggestions for pest management.

• 수산경영론집
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• 제25권1호
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• pp.37-59
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• 1994

Many studies to cope with the present problems of Korean coastal and offshore fisheries has been performed, but these were done partly in necessities and general studies for Korean inshore and offshore fisheries are in early stage. Most of these studies adopted analytical way of approach for each fishery individually and they could not reflect the effect of correlated interaction among fisheries on the several common species/stocks, and thus optimal effort allocation was impossible. To consider general fisheries and optimal effort allocation among competing mixed species, a linear programming (LP) approach is applied in this study and introduced into 16 important inshore and offshore fisheries with 13 constraining species which were chosen by annual yield order. This study is not based on the biological interaction among species (i.e., prey - predator system) but the technological interaction between species and fishing efforts. For the application of LP model in these fisheries, the standardization of fishing efforts through different fishing gears could not be successful and a new way of effort standardization through CPUE for vessel tonnage was originated. Total standardized fishing effort on a particular species i, Ei, is computed as the linear summation of standardized fishing effort generated by each fishery j. That is, (equation omitted) where $f_{j}$ is the total vessel tonnage of fishery j and aij is the coefficients contributing to the standardized fishing effort per ton for species i taken in fishery j. The total fishing effort level on species i due to both directed fishing and by - catch can thus be accounted in the aij's. Optimal effort allocation among the j fisheries may be considered a minimizing problem (minimize $\Sigma$ $f_{j}$), subject to the constraints that standardized fishing effort levels on particular species are maintained at, above, and below certain predefined levels. Fishing effort goals for individual species can be based on various biological and/or economic criteria, i.e., fishing effort level generating maximum sustainable yield and/or maximum economic yield. But in this study the $F_{0.1}$ criteria which was accepted as an approximate level for $F_{mey}$ by Outland and Boerema's (1973) study. The findings of this study are, (1) LP model can be applied to the Korean inshore and offshore fisheries giobally. (2) Through a new way of combining multiple different fisheries' efforts for a particular species together generating standardized fishing effort, Schaefer curve could be applied to the complex system successfully. (3) The results of this study for total reduction scale were mostly the same as those of prior studies, but different much from the individual scales of reduction. This study showed the necessities for exploitation of more concrete parameters to put into consideration of profitability of fisheries and social factors, and this model can be modified according to the actual constraints. Also, considering the age structure of stocks, this model can be developed into better one for better fisheries management.ent.