• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.21-29
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• 2009

This paper treats the conditions for the existence and stability properties of stationary solutions of a predator-prey interaction with self and cross-diffusion. We show that at a certain critical value a diffusion driven instability occurs, i.e. the stationary solution stays stable with respect to the kinetic system (the system without diffusion) but becomes unstable with respect to the system with diffusion and that Turing instability takes place. We note that the cross-diffusion increase or decrease a Turing space (the space which the emergence of spatial patterns is holding) compared to the Turing space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges.

• Journal of Biosystems Engineering
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• v.23 no.2
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• pp.179-186
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• 1998

This study was conducted to sense posture of an autonomous tractor using a DGPS, a gyro compass, and a potentiometer. Posture sensing system was constructed and its accuracy was evaluated. The accuracy of DGPS was evaluated under stationary and moving conditions, and the performance of the gyro compass and the potentiometer was investigated by measuring bearing and steering angles, respectively. Also, the effect of DGPS interference by obstacles was evaluated experimentally. The position accuracy was about 6.6cm(95%) under the stationary condition and 10 cm at sharp turning condition. Steering angle of the tractor could be related linearly to the output of the potentiometer that was installed on the rotating center of a knuckle arm. The positioning accuracy of the DGPS varied significantly according to the number of visible GPS satellites, but was good with more than 7 satellites. The DGPS gave bad solutions for sensing the posture of tractor when signals from satellites or the correction data from the base were interfered by obstacles.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.819-839
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• 2019

We study the stabilization of 2D g-Navier-Stokes equations in bounded domains with no-slip boundary conditions. First, we stabilize an unstable stationary solution by using finite-dimensional feedback controls, where the designed feedback control scheme is based on the finite number of determining parameters such as determining Fourier modes or volume elements. Second, we stabilize the long-time behavior of solutions to 2D g-Navier-Stokes equations under action of fast oscillating-in-time external forces by showing that in this case there exists a unique time-periodic solution and every solution tends to this periodic solution as time goes to infinity.

• East Asian mathematical journal
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• v.24 no.4
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• pp.407-414
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations with damping and convection terms, which describe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.137-142
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• 2011

In this paper we formulate a predator-prey system in two patches in which the per capita migration rate of each species is influenced only by its own density, i.e. there is no response to the density of the other one. Numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation, i. e. the stable constant steady state loses its stability and spatially non-constant stationary solutions, a pattern emerge.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.215-233
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• 2016

We consider a bistable attraction-repulsion chemotaxis system in one dimension. The study in this paper asserts that conditions for chemotactic coefficients for attraction and repulsion to show existence of stationary solutions and Hopf bifurcation in the interfacial problem as the bifurcation parameters vary are obtained analytically.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.125-141
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• 2003

This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.193-199
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• 1988

The forced vibrations of nondissipative nonlinear two-degree-of-freedom system, subjected to periodic forcing functions, are investigated by use of the method of slowly changing phase and amplitude. The first order differential equations are derived for nonrationally solutions and the coupled nonlinear algebraic equations for stationary solutions. Through investigating the response curves of the system, which are obtained numerically by using Newton-Raphson method, it is found that the resonances can occur at more than the number of degree-of-freedom of the system depending on the relation between the nonlinear spring parameters, which has no counterpart in linear systems.

• Structural Engineering and Mechanics
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• v.2 no.3
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• pp.285-294
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• 1994

Based on a fast and accurate method for the stationary random seismic response analysis for discretized structures(Lin 1992, Lin et al. 1992), a Ritz method for dealing with such responses of continuous systems in developed. This method is studied quantitatively, using cantilever shear beams for simplicity and clarity. The process can be naturally extended to deal with various boundary conditions as well as non-uniform Bernoulli-Euler beams, or even Timoshenko beams. Algorithms for both proportionally and non-proportionally damped responses are described. For all of such damping cases, it is not necessary to solve for the natural vibrations of the beams. The solution procedure is very simple, and equally efficient for a white or a non-white ground excitation spectrum. Two examples are given where various power spectral density functions, variances, covariances and second spectral moments of displacement, internal force response, and their derivatives are calculated and analyses. Some Ritz solutions are compared with "exact" CQC solutions.