• 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).

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.801-803
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• 1995

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 adaptation controllers which guarrantee 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.

• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.105-116
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• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Wind and Structures
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• v.22 no.1
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• pp.89-106
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• 2016

With an aim to assess the wind damage to urban trees in more realistic conditions, the nonlinear dynamics of structured trees subjected to strong winds with different levels is investigated in the present paper. For the logical treatment of dynamical behavior of trees, material nonlinearities of green wood associated with tree biomechanics and geometric nonlinearity of tree configuration are included. Applying simulated fluctuating wind velocity to the numerical model, the dynamical behavior of the structured tree is explored. A comparative study against the linear dynamics analysis usually involved in the previous researches is carried out. The failure wind velocity of urban trees is then defined, whereby the failure percentages of the tree components are exposed. Numerical investigations reveal that the nonlinear dynamics analysis of urban trees results in a more accurate solution of wind-induced response than the classical linear dynamics analysis, where the nonlinear effect of the tree behavior gives rise to be strengthened as increasing of the levels of wind velocity, i.e., the amplitude of 10-min mean wind velocity. The study of relationship between the failure percentage and the failure wind velocity provides a new perspective towards the vulnerability assessment of urban trees likely to fail due to wind actions, which is potential to link with the practical engineering.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.388-388
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• 2000

The complexity of nonlinear systems makes it difficult to ascertain their behavior using classical methods of analysis. Many efforts have been focused on the advanced algorithms and techniques that hold the promise of improving real-time optimal control while at the same time providing higher accuracy. In this paper, a fuzzy cell mapping method of real-time optimal control far nonlinear dynamical systems is proposed. This approach combines fuzzy logic with cell mapping techniques in order to find the optimal input level and optimal time interval in the finite set which change the state of a system to achieve a desired obiective. In order to illustrate this method, we analyze the behavior of an inverted pendulum using fuzzy cell mapping.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.12
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• pp.1155-1163
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• 2004

Extracellular signal-regulated kinase (ERK) signaling pathway is one of the mitogen-activated protein kinase (MAPK) signal transduction pathways. This pathway is known as pivotal in many signaling networks that govern proliferation, differentiation and cell survival. The ERK signaling pathway comprises positive and negative feedback loops, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. In this paper, we attempt to model the ERK pathway by considering both of the positive and negative feedback mechanisms based on Michaelis-Menten kinetics. In addition, we propose a fraction ratio model based on the mass action law. We first develop a mathematical model of the ERK pathway with fraction ratios. Secondly, we analyze the dynamical properties of the fraction ratio model based on simulation studies. Furthermore, we propose a concept of an inhibitor, catalyst, and substrate (ICS) controller which regulates the inhibitor, catalyst, and substrate concentrations of the ERK signal transduction pathway. The ICS controller can be designed through dynamical analysis of the ERK signaling transduction pathway within limited concentration ranges.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.1 no.1
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• pp.104-112
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• 2001

Simply, Nonlinear dynamics theory means the complicated and noise-like phenomena originated form nonlinearity involved in deterministic dynamical system. An almost all the natural signals have nonlinear property. However, there exist few analysis software tool or package for a research and development of applications. We develop nonlinear time series analysis simulator is to provide a common and useful tool for this purpose and to promote research and development of nonlinear dynamics theory. This simulator is consists of the following four modules such as generation module, preprocessing module, analysis module and ICA module. In this paper, we applied to Electroencephalograph (EEG), as it turned out, our simulator is able to analyze nonlinear time series. Besides, we could get the useful results using the various parameters. These results are used to diagnostic the brain diseases.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.563-572
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• 2011

In this paper, the Lie symmetry analysis is performed on the three mixed second-order PDEs, which arise in fluid dynamics, nonlinear wave theory and plasma physics, etc. The symmetries and similarity reductions of the equations are obtained, and the exact solutions to the equations are investigated by the dynamical system and power series methods. Then, the exact solutions to the general types of PDEs are considered through a variable transformation. At last, the symmetry and integration method is employed for reducing the nonlinear ODEs.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1262-1266
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• 2003

Fuzzy sliding mode controller for a class of uncertain nonlinear dynamical systems is proposed and analyzed. The controller's construction and its analysis involve sliding modes. The proposed controller consists of two components. Sliding mode component is employed to eliminate the effects of disturbances, while a fuzzy model component equipped with an adaptation mechanism reduces modeling uncertainties by approximating model uncertainties. To demonstrate its performance, the proposed control algorithm is applied to an inverted pendulum. The results show that both alleviation of chattering and performance are achieved.

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.937-956
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• 2014

The MEMS structures usually are made from silicon; consideration of the viscoelastic effect in microbeams duo to the phenomena of silicon creep is necessary. Application of the fractional model of microbeams made from viscoelastic materials is studied in this paper. Quasi-static and dynamical responses of an electrically actuated viscoelastic microbeam are investigated. For this purpose, a nonlinear finite element formulation of viscoelastic beams in combination with the fractional derivative constitutive equations is elucidated. The four-parameter fractional derivative model is used to describe the constitutive equations. The electric force acting on the microbeam is introduced and numerical methods for solving the nonlinear algebraic equation of quasi-static response and nonlinear equation of motion of dynamical response are described. The deflected configurations of a microbeam for different purely DC voltages and the tip displacement of the microbeam under a combined DC and AC voltages are presented. The validity of the present analysis is confirmed by comparing the results with those of the corresponding cases available in the literature.