• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.215-226
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• 2009

For a class of Holling type II food chain systems with biological and chemical controls, we give conditions of the local stability of prey-free periodic solutions and of the permanence of the system. Further, we show the system is uniformly bounded.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.521-533
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• 2008

We investigate a periodically forced Lotka-Volterra type predator-prey system with impulsive perturbations - seasonal effects on the prey, periodic releasing of natural enemies(predator) and spraying pesticide at the same fixed times. We show that the solutions of the system are bounded using the comparison theorems and find conditions for the stability of a stable prey-free solution and for the permanence of the system.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• Journal of computational fluids engineering
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• v.20 no.4
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• pp.58-62
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• 2015

Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.

• Journal of the Korea Computer Industry Society
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• v.3 no.5
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• pp.569-574
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• 2002

We model the torsional oscillation of a suspension bridge, which is the forced sine-Cordon equation on a bounded domain. We use finite difference method to solve nonlinear partial differential equation numerically. The partial differential equation has multiple periodic solutions. Whether the span oscillates with small or large amplitude depends oかy on its initial displacement and velocity. Moreover, we observe that the qualitative properties are consistent with the behavior observed at the Tacoma Narrows Bridge on the day of its collapse.