• 대한수학회지
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• 제44권2호
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• pp.327-342
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• 2007

In this paper, a kind of pest-predator model with impulsive effect and infinite delay is considered by the method of chain transform. By using Floquet's theorem, it is shown that there exists a globally asymptotically stable periodic pest eradication solution when the impulsive period is less than or equal to some critical value which is a directly proportional function with respect to the population of release. Furthermore, it is proved that the system is permanent if the impulsive period is larger than some critical value. Finally, the results of the corresponding systems are compared, those results obtained in this paper are confirmed by numerical simulation.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1199-1215
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• 2022

This article aims to study the dynamical behaviours of a two species model in which non-selective harvesting of a prey-predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis is used. A system of two ordinary differential equations(ODE's) has been proposed and analyzed with the predator functional response to prey density is considered as Hassell-Varley type functional responses to study the dynamics of the system. Positivity and boundedness of the system are studied. We have discussed the existence of different equilibrium points and stability of the system at these equilibrium points. We also analysed the system undergoes a Hopf-bifurcation around interior equilibrium point for a various parametric values which has very significant ecological impacts in this work. Computer simulation are carried out to validate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.

• 대한산업공학회지
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• 제29권1호
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• pp.14-20
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• 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.

• 대한수학회지
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• 제46권4호
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• pp.713-731
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• 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 the Korean Society for Industrial and Applied Mathematics
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• 제17권2호
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• pp.129-138
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• 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.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.639-651
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• 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
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• 제22권3호
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• pp.179-199
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• 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.

• 생태와환경
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• 제37권3호통권108호
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• pp.304-312
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• 2004

수 생태계 내에서 흔히 볼 수 있는 3영양단계 먹이사슬 구조를 이루는 종들이 밀도비 의존 모델로써 구현 될 때 외부 환경에 대해서 어떻게 반응하는지를 연구하였다. 환경 요인은 주기적 요인과 일반적 노이즈 두 부분으로 나누었다. 주기적 요인이 온도로써 대표되었을 때 온도변이를 바이어스와 주기로 나누었고, 기타 복합적인 노이즈는 가우스 분포로 나타내었다. 온도변이 바이어스 ${\varepsilon}$, 온도주기 ${\Omega}$, 및 가우스 노이즈 크기 ${\'{O}}$가 서로 결합하여 3영양단계 먹이사슬에서 개체군 멸절을 포함한 다양한 개체군 동태를 보여 주었다. 변수의 적절한 값에 따라 '안정된 제한 사이클'이나 '이상한 끌개'를 보여 주었으며, 전체적으로 개체군 동태는 환경 변수에 따라 민감하게 반응하였고, 포식자 및 최상위포식자 개체군의 멸절시간이 조절되었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제8권1호
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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.

• 대한수학회논문집
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• 제23권2호
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• pp.211-227
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• 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.