• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.299-312
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• 2009

In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with nonautonomous N-dimensional impulsive Lotka Volterra competitive systems with dispersions and fixed moments of impulsive perturbations. By using the techniques of piecewise continuous Lyapunov's functions new sufficient conditions for the global exponential stability of the unique almost periodic solutions of these systems are given.

• 대한수학회지
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• 제53권5호
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• pp.969-990
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• 2016

We derive a sampling theorem associated with first order self-adjoint eigenvalue problem with a finite rank perturbation. The class of the sampled integral transforms is of finite Fourier type where the kernel has an additional perturbation.

• Bulletin of the Korean Chemical Society
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• 제21권12호
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• pp.1213-1216
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• 2000

Localized structures with fronts connecting a Turing patterns and Hopf oscillations are found in discrete reaction-diffusion system. The Chorite-Iodide-Malonic Acid (CIMA) reaction model is used for a reaction scheme. Localized structures in discrete reaction-diffusion system have more diverse and interesting features than ones in continuous system. Various localized structures can be obtained when a single perturbation is applied with variation of coupling strength of two intermediates. Roles of perturbations are not so simple that perturbations are sources of both Turing patterns and Hopf oscillating domains, and spatial distribution of them is determined by strength of a perturbation applied initially.

• Smart Structures and Systems
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• 제9권3호
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• pp.231-251
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• 2012

The stochastic optimal control for a piezoelectric spherically symmetric shell subjected to stochastic boundary perturbations is constructed, analyzed and evaluated. The stochastic optimal control problem on the boundary stress output reduction of the piezoelectric shell subjected to stochastic boundary displacement perturbations is presented. The electric potential integral as a function of displacement is obtained to convert the differential equations for the piezoelectric shell with electrical and mechanical coupling into the equation only for displacement. The displacement transformation is constructed to convert the stochastic boundary conditions into homogeneous ones, and the transformed displacement is expanded in space to convert further the partial differential equation for displacement into ordinary differential equations by using the Galerkin method. Then the stochastic optimal control problem of the piezoelectric shell in partial differential equations is transformed into that of the multi-degree-of-freedom system. The optimal control law for electric potential is determined according to the stochastic dynamical programming principle. The frequency-response function matrix, power spectral density matrix and correlation function matrix of the controlled system response are derived based on the theory of random vibration. The expressions of mean-square stress, displacement and electric potential of the controlled piezoelectric shell are finally obtained to evaluate the control effectiveness. Numerical results are given to illustrate the high relative reduction in the root-mean-square boundary stress of the piezoelectric shell subjected to stochastic boundary displacement perturbations by the optimal electric potential control.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.700-705
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• 2005

The purpose of this project is the derivation and development of techniques for the new estimation of robustness for the systems having uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. Bounded means the uncertainties are with same positive/negative range. The number of uncertainties will be the degree of freedoms in the calculation of the stability region. This is so called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, the selection of Lyapunov candidate function is of various forms. In this paper, the quadratic form is selected. this generated techniques has been demonstrated by recent research interest in the area of robust control design and confirms that estimation of robustness bounds will be improved upon those obtained by results of the original Lyapunov method. In this paper, the symbolic algebraic procedures are utilized and the calculating errors are reduced in the numerical procedures. The application of numerical procedures can prove the improvements in estimations of robustness for one-and more structured perturbations. The applicable systems is assumed to be linear with time-varying with nonlinear bounded perturbations. This new techniques will be extended to other nonlinear systems with various forms of uncertainties, especially in the nonlinear case of the unstructured perturbations and also with various control method.

• Wind and Structures
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• 제7권4호
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• pp.265-280
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• 2004

This paper presents some fundamental results on the dynamics of the periodic Karman wake behind a circular cylinder. The wake is treated like a dynamical system. External forcing is then introduced and its effect investigated. The main result obtained is the following. Perturbation of the wake, by controlled cylinder oscillations in the flow direction at a frequency equal to the Karman vortex shedding frequency, leads to instability of the Karman vortex structure. The resulting wake structure oscillates at half the original Karman vortex shedding frequency. For higher frequency excitation the primary pattern involves symmetry breaking of the initially shed symmetric vortex pairs. The Karman shedding phenomenon can be modeled by a nonlinear oscillator. The symmetrical flow perturbations resulting from the periodic cylinder excitation can also be similarly represented by a nonlinear oscillator. The oscillators represent two flow modes. By considering these two nonlinear oscillators, one having inline shedding symmetry and the other having the Karman wake spatio-temporal symmetry, the possible symmetries of subsequent flow perturbations resulting from the modal interaction are determined. A theoretical analysis based on symmetry (group) theory is presented. The analysis confirms the occurrence of a period-doubling instability, which is responsible for the frequency halving phenomenon observed in the experiments. Finally it is remarked that the present findings have important implications for vortex shedding control. Perturbations in the inflow direction introduce 'control' of the Karman wake by inducing a bifurcation which forces the transfer of energy to a lower frequency which is far from the original Karman frequency.

• 천문학회보
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• 제39권2호
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• pp.78.1-78.1
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• 2014

An ionization front (IF) surrounding an H II region is a sharp interface through which a cold neutral gas makes transition to a warm ionized phase by absorbing UV photons from central massive stars. We investigate the structure and instability of a plane-parallel D-type IF threaded by magnetic fields parallel to the front. We find that magnetic fields increase the maximum propagation speed of the IFs, while reducing the expansion factor, defined as the density ratio of neutral to ionized phases. IFs become unstable to distortional perturbations due to gas expansion across the fronts, exactly analogous to the Darrieus-Landau instability of ablation fronts in terrestrial flames. The growth rate of the IF instability is proportional linearly to the perturbation wavenumber as well as the upstream flow speed. The IF instability is stabilized by gas compressibility and becomes completely quenched when the front is D-critical. The instability is also stabilized by magnetic pressure when the perturbations propagate in the direction perpendicular to the fields. When the perturbations propagate in the direction parallel to the fields, on the other hand, it is magnetic tension that reduces the growth rate, completely suppressing the instability when ${\beta}$ < 1.5, with ${\beta}$ denoting the square of the ratio of the sound speed to the Alfven speed in the pre-IF region. When the front experiences an acceleration, the IF instability cooperates with the Rayleigh-Taylor instability to make the front more unstable. We discuss potential effects of IF instability on the evolution and dynamics of IFs in the interstellar medium.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 추계학술대회 논문집
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• pp.1066-1069
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• 2002

Dynamic postural control varies with the environmental context, specific task and intentions of the subject. In this paper, dynamic postural control against forward-backward perturbations of a platform was estimated using tri-axial accelerometers and a force plate. Ten young healthy volunteers stood upright in comfortable condition on the perturbation system which was controlled by an AC servo motor. With anterior-posterior perturbations, movements of ankle, knee and hip Joints were obtained by tri-axial accelerometers. and ground reaction forces with corresponding displacements of the center of pressure(CoP) by the force plate. The result showed that the ankle moved first and the trunk forward, which implies that the mechanism of the dynamic postural control in forward-backward perturbations, occurred in the procedure of the ankle, the knee and the hip. Knee flexion and hip extension in the period of acceleration, constant velocity and deceleration phase is very important fur the balance recovery. These responses depends on the magnitude and timing of the perturbation. From the present study the accelerometry-system appears to be a promising tool for understanding kinematic accelerative In response to a transient platform perturbation. A more through understanding of balance recovery mechanism may aid in designing methods for reducing falls and the resulting injuries.

• 대한기계학회논문집B
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• 제32권6호
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• pp.413-420
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• 2008

The unsteady heat release characteristics play a significant role in combustion instabilities observed in low emissions gas turbine combustors. Such combustion instabilities are often caused by coupling mechanisms between unsteady heat release rates and acoustic perturbations. A generalized model of the turbulent flame response to acoustic perturbations is analytically formulated by considering a distributed heat release along a curved mean flame front and using the flame's kinematic model that incorporates the turbulent flame development. The effects of the development of flame speed on the flame transfer functions are examined by calculating the transfer functions with a constant or developing flame speed. The flame transfer function due to velocity fluctuation shows that, when a developing flame speed is used, the transfer function magnitude decreases faster with Strouhal number than the results with a constant flame speed at low Strouhal numbers. The flame transfer function due to mixture ratio fluctuation, however, exhibits the opposite results: the transfer function magnitude with a developing flame speed increases faster than that with a constant flame speed at low Strouhal numbers. Oscillatory behaviors of both transfer function magnitudes are shown to be damped when a developing flame speed is used. Both transfer functions also show similar behaviors in the phase characteristics: The phases of both transfer functions with a developing flame speed increase more rapidly than those with a constant flame speed.

• Kyungpook Mathematical Journal
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• 제30권2호
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• pp.195-204
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• 1990