Browsing by Author "Hsu, Mao-Yuan"

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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 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.