• Journal of the Korean Mathematical Society
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• v.28 no.2
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• pp.215-228
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• 1991

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.1-16
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• 2017

In this paper we study a four dimensional tourism-based social-ecological dynamical system. In fact we analyse tourism profitability, compatibility and sustainability by using bifurcation theory in terms of structural properties of attractors of system. For this purpose first we transformed it into a three dimensional system such that the reduced system is the extended and modified model of the previous three dimensional models suggested for tourism with the same dimension. Then we investigate transcritical, pitchfork and saddle-node bifurcation points of system. And numerically by finding some branches of stable equilibria for system show the profitability of tourism industry. Then by determining the Hopf bifurcation points of system we find a family of stable attractors for that by numerical techniques. Finally we conclude the existence of these stable limit cycles implies profitability and compatibility and then the sustainability of tourism.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.9
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• pp.859-866
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• 2010

Nonlinear dynamics of pulsating instability-diffusional-thermal instability with Lewis numbers sufficiently higher than unity-in counterflow diffusion flames, is numerically investigated by imposing a Damkohler number perturbation. The flame evolution exhibits three types of nonlinear behaviors, namely, decaying pulsating behavior, diverging behavior (which leads to extinction), and stable limit-cycle behavior. The stable limit-cycle behavior is observed in counterflow diffusion flames, but not in diffusion flames with a stagnant mixing layer. The critical value of the perturbed Damkohler number, which indicates the region where the three different flame behaviors can be observed, is obtained. A stable simple limit cycle, in which two supercritical Hopf bifurcations exist, is found in a narrow range of Damkohler numbers. As the flame temperature is increased, the stable simple limit cycle disappears and an unstable limit cycle corresponding to subcritical Hopf bifurcation appears. The period-doubling bifurcation is found to occur in a certain range of Damkohler numbers and temperatures, which leads to extend the lower boundary of supercritical Hopf bifurcation.

• The Transactions of the Korean Institute of Power Electronics
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• v.5 no.4
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• pp.394-402
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• 2000

This paper proposes a bifurcation theory method applied for voltage stability analysis and shows the improvement of voltage stability by attaching the FACTS devices in the power system. A power system is generally expressed by a set of equations of highly nonlinear dynamical system which includes system parameters(real or reactive power). Sometimes variation of parameters in the system may result in complication behaviors which give rise to system instability. The addition of FACTS increases the range of voltage stability in the power system. The effect of FACTS which improves voltage stability are illustrated in the case studies by delaying of Unstable Hopf Bifurcation and Saddle Node Bifurcation.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1185-1202
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• 2010

In this paper, we have studied the dynamical behaviour such as boundedness, local and global stabilities, bifurcation of a single species population affected by environmental toxicant and population toxicant. We have also studied the effect of discrete delay of the environmental toxicant on the instantaneous growth rates of the population biomass and population toxicant due to incubation period. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.309-312
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• 1997

The dynamic characteristics of a continuous MMA/MA free-radical solution copolymerization reactor were studied. A mathematical model was developed and kinetic parameters which had been estimated in the previous work were used. With this model, bifurcation diagrams were constructed with various parameters as the bifurcation parameter to predict the region of stable operating conditions and to enhance the controller performance. It was shown that the steady-state multiplicity existed over wide ranges of residence time and jacket inlet temperature. Periodic solution branches were found to emanated from Hopf bifurcation points. Under certain conditions isola was also observed, which would result in poor performance of feedback controllers.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.447-470
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• 2016

Limit cycle oscillations (LCO) as well as nonlinear aeroelastic analysis of a swept aircraft wing with cubic restoring moments in the pitch degree of freedom is investigated. The unsteady aerodynamic loading applied on the wing is modeled by using the strip theory. The harmonic balance method is used to calculate the LCO frequency and amplitude for the swept wing. Finally the super and subcritical Hopf bifurcation diagrams are plotted. It is concluded that the type of bifurcation and turning point location is sensitive to the system parameters such as wing geometry and sweep angle.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1994-2003
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• 2003

The vibration of a flexible cantilever tube with nonlinear constraints when it is subjected to flow internally with fluids is examined by experimental and theoretical analysis. These kinds of studies have been performed to find the existence of chaotic motion. In this paper, the important parameters of the system leading to such a chaotic motion such as Young's modulus and the coefficient of viscoelastic damping are discussed. The parameters are investigated by means of system identification so that comparisons are made between numerical analysis using the design parameters and the experimental results. The chaotic region led by several period-doubling bifurcations beyond the Hopf bifurcation is also re-established with phase portraits, bifurcation diagram and Lyapunov exponent so that one can define optimal parameters for system design.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.495-500
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• 2003

The vibration of a flexible cantilever tube with nonlinear constraints when it is subjected to flow internally with fluids is examined by experiment and theoretical analysis. These kind of studies have often been performed that finds the existence of chaotic motion. In this paper, the important parameters of the system leading to such a chaotic motion such as Young's modulus and coefficient of viscoelasticity in tube material are discussed. The parameters are investigated by means of a system identification so that comparisons are made between numerical analysis using the parameters of a handbook and the experimental results. The chaotic region led by several period-doubling bifurcations beyond the Hopf bifurcation is also re-established with phase portraits and bifurcation diagram so that one can define optimal parameters for system design.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.9
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• pp.2965-2972
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• 1996

Transitional flow in an obstructed channel is investigated using numerical simulation. Two-dimensional thin obstacles are mounted symmetrically in the vertical direction and periodically in the streamwise direction. Flow separation occurs at the tip of the sharp obstacles. Depending on the Reynolds number, the flow undergoes Hopf bifurcation as the primary instability leading to a two-dimensional unsteady periodic solution. At higher Reynolds numbers, the unsteady solution exhibits a symmetry-breaking bifurcation which results in an unsteady asymmetric solution. The results are compared with experiments currently available, and show a good agreement.