• 대한수학회논문집
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• 제24권2호
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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.

• 호남수학학술지
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• 제30권3호
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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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• 제16권4호
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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 $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• 한국전산유체공학회지
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• 제20권4호
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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.

• 한국컴퓨터산업학회논문지
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• 제3권5호
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• pp.569-574
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• 2002

유계된 정의역에서 sine-Gordon 방정식인 현수교의 과격한 운동의 모델을 만든다. 유한 차분법을 이용하여 비선형 미분방정식을 수치 해석학적으로 풀다. 이 미분방정식은 다중 주기근을 가지고 있다. 다리가 큰 진폭이나 작은 진폭으로 진동하는 것은 초기의 변위와 속도에만 달려있다. 게다가, 많은 현상들이 Tacoma Narrows가 붕괴된 날에 관찰되는 것과 일치하고 있다.