• Journal of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.713-731
• /
• 2009

In this paper, a three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay ${\tau}$ passes though a sequence of critical values. The estimation of the length of delay to preserve stability has also been calculated. Numerical simulation with a hypothetical set of data has been done to support the analytical findings.

• Journal of Species Research
• /
• v.5 no.3
• /
• pp.375-380
• /
• 2016

Mites of the genus Antennoseius of family Ascidae are free-living soil predator mostly observed on the open grass field. In Korea, only two species, Antennoseius imbricatus Ishikawa, 1969 and A. japonicus Ishikawa, 1979 were reported in 1990s. Recent series of soil acarine biodiversity survey in Gyeongbuk province during 2009-2015. We recovered a new record of Antennoseius avius (Karg, 1976) to Korean inventory from riparian grassland. Detailed description of the species as well as the identification key to the genus and species were provided.

• Korean Journal of Microbiology
• /
• v.23 no.1
• /
• pp.49-55
• /
• 1985

The survival of Escherichia coli in river water was comparatively studied by laboratory and in sity study methods. The survival by two methods was evaluated as a function of E. coli strain, indigeneous predator, level of water pollution, and water temperature in different season. The survival rate of E. coli examined by laboratory method was lower than that by in situ method. That was found to be due to the fact that higher number of predator was maintained in labortory study than in in situ study. The survival rates of E. coli in gradually polluted river waters could be differentiated by in situ study, but not by laboratory study. Therefore, an in situ method rather than labortory method was thought to be a choice of study method for the survival of E. coli in river waters.

• Communications of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.211-227
• /
• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.219-231
• /
• 2003

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by taking E(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.639-651
• /
• 2009

In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.2
• /
• pp.129-138
• /
• 2013

A spatio-temporal models as systems of ODE which describe two-species Beddington - DeAngelis type predator-prey system living in a habitat of two identical patches linked by migration is investigated. It is assumed in the model that the per capita migration rate of each species is influenced not only by its own but also by the other one's density, i.e. there is cross diffusion present. We show that a standard (self-diffusion) system may be either stable or unstable, a cross-diffusion response can stabilize an unstable standard system and destabilize a stable standard system. For the diffusively stable model, numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross migration response is an important factor that should not be ignored when pattern emerges.

• Applied Microscopy
• /
• v.46 no.2
• /
• pp.89-92
• /
• 2016

The bluegill Lepomis macrochirus is an invasive species, not native to Korea, introduced for aquaculture. This species is ranked as a new top predator due to its massive aquatic carnivorous and herbivorous nature by acute vision and the absence of a natural enemy. The visual cells of the retina of L. macrochirus are composed of short single cones and equal double cones and long and bulky rods by light and electron microscopes. In particular, the cones show a regular square mosaic arrangement. This pattern is widely considered as a strong predator. With regard to the visual system, this mosaic pattern may closely be related to a dynamic visual acuity to track and hunt prey.

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

• Journal of Korean Institute of Industrial Engineers
• /
• v.29 no.1
• /
• pp.14-20
• /
• 2003

The purpose of this paper is an attempt to analyze the dynamic relationship between KSE and KOSDAQ, two competing markets in Korean stock market, in the viewpoint of competition. Lotka-Volterra model, one of well-known competitive diffusion model, is adopted to represent the competitive situations of Korean stock market and it is estimated using daily empirical index data of KSE and KOSDAQ during 1997~2001. The results show that there existed a predator-prey relationship between two markets in which KSE acted as a predator right after the emergence of KOSDAQ. This interaction was altered to a symbiotic relationship and finally to the pure competition relationship. We also perform an equilibrium analysis of the estimated Lotka-Volterra equations and, as a result, it is found that there is a market index equilibrium point that would be stable in the latest relationship.