• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.439-445
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• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.873-894
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• 2021

In this paper, we consider the Gudnason model of 𝒩 = 2 supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.281-295
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• 2005

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.253-263
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• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1225-1248
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• 2011

The present paper is concerned with a two-competitor/oneprey population system with Holling type-II functional response and two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Particularly, by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs) explicit formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are derived. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.193-207
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• 2010

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.267-276
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• 2017

The purpose of this paper is to investigate the local asymptotic stability of equilibria, the periodic nature of solutions, the existence of unbounded solutions and the global behavior of solutions of the fractional difference equation $$x_{n+1}=\frac{^{{\alpha}x}n-1(k+1)}{{\beta}+{\gamma}x^p_{n-k}x^q_{n-(k+2)}}$$, $$n=0,1,{\dots}$$ where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-(k+2)}$,$x_{-(k+1)}$, ${\dots}$, $x_{-1}$, $x_0{\in}\mathb{R}^+$.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.71-82
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• 2009

In this paper, a stage-structured predator-prey system with impulsive perturbations and time delays is presented to investigate the ecological problem of how a pest population and natural enemy population can coexist. Sufficient conditions are obtained using a discrete dynamical system determined by a stroboscopic map, which guarantee that a 'predator-extinction' periodic solution is globally attractive. When the impulsive period is longer than some time threshold or the impulsive harvesting rate is below a control threshold, the system is permanent. Our results provide some reasonable suggestions for pest management.

• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.4
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• pp.3-13
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• 1989

In recent towing tank experiments, it has been observed that a ship moving near the critical speed $\sqrt{gh}$(g=gravitational acceleration, h=water depth) radiates solitons upstream in an almost periodic manner. As a ,consequence, the ship experiences considerable changes in resistance, trim and sinkage, or better known as squat. Mei and Choi(1987) developed a nonlinear theory for a slender ship by using the method of matched asymptotic expansions. For a certain class of channel width and ship slenderness, they found that the waves generated can be described by an inhomogeneous Korteweg-de Vries(KdV) equation. The leading-order solution properly predicts solitons propagating upstream, but it fails to render three-dimensional waves in the wake. In this paper a new approach has been made by choosing a different class of channel width and ship slenderness. The wave equation in the farfield turns out to be a homogeneous Kadomtsev-Petviashvili(KP) equation, which predicts solitons upstream and three-dimensional waves in the wake. Numerical results for the wave resistance, sinkage and trim reflect the experimentally identified phenomena.