Browsing by Author "Ge, Zheng-Ming"

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A new study of chaotic behavior and the existence of Feigenbaum's constants in fractional-degree Yin-Yang Henon maps
(2013-10-01)
Ho, Chun-Yen
;
Chen, Hsien-Keng
;
Ge, Zheng-Ming
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, we firstly develop fractional-degree H,non maps with increasing and decreasing argument n. Yin and Yang are two fundamental opposites in Chinese philosophy. Yin represents the moon and is the decreasing, negative, historical, or feminine principle in nature, while Yang represents the sun and is the increasing, positive, contemporary, or masculine principle in nature. Chaos produced by increasing n is called Yang chaos, that by decreasing n Yin chaos, respectively. The simulation results show that chaos appears via positive Lyapunov exponents, bifurcation diagrams, and phase portraits. In order to examine the existence of chaotic behaviors in fractional-degree Yin-Yang H,non maps, Feigenbaum's constants are measured in this paper. It is found that the Feigenbaum's constants in fractional-degree Yin-Yang H,non maps are of great precision to the first and second Feigenbaum's constants. A detailed analysis of the chaotic behaviors is also performed for the fractional-degree H,non maps with increasing (Yang) and decreasing (Yin) argument n.
Advanced dynamics for variable mass systems
(高立圖書, 1997)
Ge, Zheng-Ming
Advanced dynamics for variable mass systems and topics on dynamics
(Gau Lih, 2002)
Ge, Zheng-Ming
Anti-control of chaos of single time-scale brushless DC motor
(2006-09-15)
Ge, Zheng-Ming
;
Chang, Ching-Ming
;
Chen, Yen-Sheng
;
機械工程學系
;
Department of Mechanical Engineering
Anti-control of chaos of single time-scale brushless DC motors is studied in this paper. In order to analyse a variety of periodic and chaotic phenomena, we employ several numerical techniques such as phase portraits, bifurcation diagrams and Lyapunov exponents. Anti-control of chaos can be achieved by adding an external constant term or an external periodic term.
Anticontrol of chaos of the fractional order modified van der Pol systems
(2007-04-15)
Ge, Zheng-Ming
;
Zhang, An-Ray
;
機械工程學系
;
Department of Mechanical Engineering
Anticontrol of chaos of fractional order modified van der Pol systems is studied. Addition of a constant term and addition of k vertical bar x vertical bar sinx term where x is a state of the system are used to anticontrol the system effectively. By applying numerical results, phase portrait, Poincare maps and bifurcation diagrams a variety of the phenomena of the chaotic motion can be presented. Finally, it can be find that chaos under these procedures exists in the fractional order systems of a modified van der Pol system. (c) 2006 Elsevier Inc. All rights reserved.
Bifurcation, chaos and chaos control of mechanical systems
(Gau Lih Book, 2001)
Ge, Zheng-Ming
Chaos and chaos control for a two-degree-of-freedom heavy symmetric gyroscope
(2007)
Ge, Zheng-Ming
;
Hsiao, Chun-Lai
;
Chen, Yen-Sheng
;
Chang, Ching-Ming
;
機械工程學系
A two-degree-of-freedom heavy symmetric gyroscope is studied in this paper. This system is forced by harmonically periodic vertical vibration to enrich dynamic behaviors. Because of the nonlinear terms of the system, the system exhibits chaotic motion. By applying various numerical results, such as phase portraits, Poincare maps, time history and power spectrum analysis, the behaviors of the periodic and chaotic motion are presented. The effects of the change of parameters in the system can be found in the bifurcation diagrams and parametric diagrams. The method of Lyapunov exponents is used to identify the chaos or regular motions of the systems. Next, nine controlling methods are applied into the systems, in which the modified open-plus-closed-loop control is firstly proposed. Open and feedback loops of controls are both studied. It is found that each controller can effectively control the chaotic orbits to the regular ones.
Chaos control for rigid body systems
(Gau Lih, 2002)
Ge, Zheng-Ming
Chaos control of new Ikeda-Lorenz systems by GYC partial region stability theory
(2009-08-01)
Ge, Zheng-Ming
;
Ho, Chun-Yen
;
Li, Shih-Yu
;
Chang, Ching-Ming
;
機械工程學系
A new strategy to achieve chaos control by GYC partial region stability theory is proposed. By using the GYC partial region stability theory, the Lyapunov function is a simple linear homogeneous function of error states, the controllers are more simple and have less simulation error because they are in lower degree than that of traditional controllers. Simulation results for a new Ikeda-Lorenz system show the effectiveness of this strategy. Copyright (C) 2008 John Wiley & Sons, Ltd.
Chaos control of new Mathieu-Van der Pol systems with new Mathieu-Duffing systems as functional system by GYC partial region stability theory
(2009-11-01)
Ge, Zheng-Ming
;
Li, Shih-Yu
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, a new strategy by using GYC partial region stability theory is proposed to achieve chaos control. Using the GYC partial region stability theory, the new Lyapunov function used is a simple linear homogeneous function of error states and the lower order controllers are much more simple and introduce less simulation error. Numerical simulations are given for new Mathieu-Van der Pol system and new Mathieu-Duffing system to show the effectiveness of this strategy. (C) 2009 Elsevier Ltd. All rights reserved.
Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems
(2008-05-01)
Ge, Zheng-Ming
;
Hsu, Mao-Yuan
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pot chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pot system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pot system. (c) 2006 Elsevier Ltd. All rights reserved.
Chaos generalized synchronization of an inertial tachometer with new Mathieu-Van der Pol systems as functional system by GYC partial region stability theory
(2012-03-01)
Yang, Cheng-Hsiung
;
Chen, Tsung-Wen
;
Li, Shih-Yu
;
Chang, Ching-Ming
;
Ge, Zheng-Ming
A new strategy to achieve generalized chaos synchronization by GYC partial region stability theory is proposed. By using the GYC partial region stability theory the Lyapunov function is a simple linear homogeneous function of error states and the controllers are more simple and introduce less simulation error because they are in lower order than that of traditional controllers. In simulation examples, an inertial tachometer system and Mathieu-Van der Pol system are used. (C) 2011 Elsevier B.V. All rights reserved.
Chaos generalized synchronization of new Mathieu-Van der Pol systems with new Duffing-Van der Pol systems as functional system by GYC partial region stability theory
(2011-11-01)
Ge, Zheng-Ming
;
Li, Shih-Yu
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, a new strategy by using GYC partial region stability theory is proposed to achieve generalized chaos synchronization. via using the GYC partial region stability theory, the new Lyapunov function used is a simple linear homogeneous function of states and the lower order controllers are much more simple and introduce less simulation error. Numerical simulations are given for new Mathieu-Van der Pol system and new Duffing-Van der Pol system to show the effectiveness of this strategy. (C) 2011 Elsevier Inc. All rights reserved.
Chaos in a fractional order modified Duffing system
(2007-10-01)
Ge, Zheng-Ming
;
Ou, Chan-Yi
;
機械工程學系
;
Department of Mechanical Engineering
in this paper, the chaotic behaviors in a fractional order modified Duffing system are studied numerically by phase portraits, Poincare maps and bifurcation diagrams. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0, 1], based on frequency domain arguments. The total system orders found for chaos to exist in such systems are 1.8, 1.9, 2.0 and 2.1. (c) 2005 Elsevier Ltd. All rights reserved.
Chaos in a generalized van der Pol system and in its fractional order system
(2007-08-01)
Ge, Zheng-Ming
;
Hsu, Mao-Yuan
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, chaos of a generalized van der Pol system with fractional orders is studied. Both nonautonomous and autonomous systems are considered in detail. Chaos in the nonautonomous generalized van der Pol system excited by a sinusoidal time function with fractional orders is studied. Next, chaos in the autonomous generalized van der Pol system with fractional orders is considered. By numerical analyses, such as phase portraits, Poincare maps and bifurcation diagrams, periodic, and chaotic motions are observed. Finally, it is found that chaos exists in the fractional order system with the order both less than and more than the number of the states of the integer order generalized van der Pol system. (C) 2006 Elsevier Ltd. All rights reserved.
Chaos in a modified van der Pol system and in its fractional order systenis
(2007-06-01)
Ge, Zheng-Ming
;
Zhang, An-Ray
;
機械工程學系
;
Department of Mechanical Engineering
Chaos in a modified van der Pot system and in its fractional order systems is studied in this paper. It is found that chaos exists both in the system and in the fractional order systems with order from 1.8 down to 0.8 much less than the number of states of the system, two. By phase portraits, Poincare maps and bifurcation diagrams, the chaotic behaviors of fractional order modified van der Pot systems are presented. (c) 2005 Elsevier Ltd. All rights reserved.
Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems
(2007-04-01)
Ge, Zheng-Ming
;
Yi, Chang-Xian
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, the chaotic behaviors of a nonlinear damped Mathieu system and of a nonlinear nano resonator system with integral orders and with fractional orders are studied. By applying numerical analyses such as phase portraits, Poincare maps and bifurcation diagrams, the periodic and chaotic motions are observed. It is found that chaos exists both in the nonlinear damped Mathieu system and in the integral order and fractional order nano resonator systems. (c) 2005 Elsevier Ltd. All rights reserved.
Chaos synchronization and chaos control of quantum-CNN chaotic system by variable structure control and impulse control
(2010-06-01)
Yang, Cheng-Hsiung
;
Ge, Zheng-Ming
;
Chang, Ching-Ming
;
Li, Shih-Yu
;
機械工程學系
In this paper, we derive some less stringent conditions for the exponential and asymptotic stability of impulsive control systems with impulses at fixed times These conditions are then used to design an impulsive control law for the Quantum Cellular Neural Network chaotic system, which drives the chaotic state to zero equilibrium and synchronizes two chaotic systems. An active sliding mode control method is synchronizing two chaotic systems and controlling chaotic state to periodic motion state And a sufficient condition is drawn for the robust stability of the error dynamics, and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy. (C) 2010 Published by Elsevier Ltd
Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control
(2009-10-30)
Ge, Zheng-Ming
;
Yang, Cheng-Hsiung
;
機械工程學系
;
Department of Mechanical Engineering
By the method of quadratic optimum control, a quadratic optimal regulator is used for synchronizing two complex chaotic systems in series form. By this method the least error with less control energy is achieved, and the optimization on both energy and error is realized synthetically. The simulation results of two Quantum-CNN chaos systems in series form prove the effectiveness of this method. Finally, chaotization of the system is given by optimal control. (C) 2009 Elsevier Ltd. All rights reserved.
Chaos synchronization by variable strength linear coupling and Lyapunov function derivative in series form
(2008-12-15)
Ge, Zheng-Ming
;
Tsen, Pu-Chien
;
機械工程學系
;
Department of Mechanical Engineering
A new general strategy to achieve chaos synchronization by variable strength linear Coupling without another active control is proposed. They give the criteria of chaos synchronization for two identical chaotic systems and two different chaotic dynamic systems with variable strength linear coupling. In this method, the time derivative of Lyapunov function in series form is firstly used. Lorenz system, Duffing system, Rossler system and Hyper-Rossler system are presented as simulated examples. (C) 2007 Elsevier Ltd. All rights reserved.