• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.4
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• pp.379-387
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• 1999

In general, solving or analyzing nonilinear dynamical equations is very difficult and requires special techniques. To avoid these difficulties, systems are generally linearized in an attempt to predict their begavior. These linearized equations, however, may not predict true system behavior. Therefore, the nonlinear dynamical analysis using bifurcation theory may become a fundamental framework in understanding nonlinear situation in power systems. In this paper, we propose a systematic procedure based on a bifurcation theory to analyze nonlinear behaviors in power systems. We show usefulness of our procedure by applying 3-bus model system. In addition, we consider nonlinear model of SMES and verify the effect of SMES in power system's nonlinear behaviors.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.3
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• pp.325-331
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• 2018

This paper deals with the dynamical analysis of a vessel that leads to capsize in regular beam seas. The complete investigation of nonlinear behaviors includes sub-harmonic motion, bifurcation, and chaos under variations of control parameters. The vessel rolling motions can exhibit various undesirable nonlinear phenomena. We have employed a linear-plus-cubic type damping term (LPCD) in a nonlinear rolling equation. Using the fourth order Runge-Kutta algorithm with the phase portraits, various dynamical behaviors (limit cycles, bifurcations, and chaos) are presented in beam seas. On increasing the value of control parameter ${\Omega}$, chaotic behavior interspersed with intermittent periodic windows are clearly observed in the numerical simulations. The chaotic region is widely spread according to system parameter ${\Omega}$ in the range of 0.1 to 0.9. When the value of the control parameter is increased beyond the chaotic region, periodic solutions are dominant in the range of frequency ratio ${\Omega}=1.01{\sim}1.6$. In addition, one more important feature is that different types of stable harmonic motions such as periodicity of 2T, 3T, 4T and 5T exist in the range of ${\Omega}=0.34{\sim}0.83$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.3
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• pp.755-760
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• 1990

VAXIMA is a computer software which gives us results in terms of parameters. We use VAXIMA to analyze quantitatively a conservative dynamical system with cubic and quintic nonlinear terms. The system is described by a nonlinear second-order autonomous ordinary differential equation. Using the Lindstedt-Poincare method, we obtain period-amplitude characteristics. In order to check the validity of the approximate solution, we integrate numerically the equation of motion.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5B
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• pp.439-446
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• 2006

In the present study, we applied wavelet transform to decompose the hydro-meteorological data such as precipitation and temperature into the components with different return periods with a primary objective for extraction of nonlinear dynamical component. For the transform, we used the Daubechies wavelet of order 9 ('db9') as a basis function. Also, we applied the correlation dimension analysis to determine whether or not the detail and approximation components at the respective decomposition stage with the increasing of scale in the wavelet transform reveal the nonlinear dynamical characteristics. In other words, we proposed the combined use of the wavelet transform and the correlation dimension analysis as methodology to extract the nonlinear dynamical component from the hydro-meteorological data. The derived result has shown the method proposed in the present study is suitable for the segregation and extraction of the nonlinear dynamical component which is, in general, difficult to reveal by using the raw data.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.521-535
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• 2023

In this work, some various types of Dissipativity in random dynamical systems are introduced and studied: point, compact, local, bounded and weak. Moreover, the notion of random Levinson center for compactly dissipative random dynamical systems presented and prove some essential results related with this notion.

• Journal of Biomedical Engineering Research
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• v.14 no.4
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• pp.379-386
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• 1993

This paper describes design of a Chaos analyser and its applications to analysis of nonlinear characteristirs of ECG. The proposed system can easily distinguish chaotic system among the various dynamical systems by chaotic quantitative and qualitative analysis and also chaotic characteristics which represents states of nonlinear dynamical system. And we have also proposed new possibilities to recognize abnormal state of ECG signal using the chaotic characteristics.

• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.669-683
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• 2003

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

• Structural Engineering and Mechanics
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• v.23 no.6
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.2
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• pp.101-101
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• 1996

This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptaion controllers which guarantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.883-902
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• 2012

In this work we deal with a nonlinear dynamical system, namely the wastewater treatment model. We proceed to a dynamical analysis of the model. Invariance, boundness, controllability and the sensitivity with respect the initial conditions are studied. On the other hand, using the nonsmooth analysis tools, we look for the viability of the model, that is, the necessary and sufficient conditions under which trajectories move in a suitable time-moving sets, to avoid the washing problem (died of bacteria).