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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24433

Title: A Chaos Detectable and Time Step-Size Adaptive Numerical Scheme for Non-Linear Dynamic Systems
Authors: Yung-Wei Chen;Chein-Shan Liu;Jiang-Ren Chang
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
Date: 2007-02-06
Issue Date: 2011-10-20T08:12:18Z
Publisher: Journal of Sound and Vibration
Abstract: Abstract:The first step in investigation the dynamics of a continuous timesystem described by ordinary differential equations is to integrate them to obtain trajectories. In this paper, we convert the group-preserving scheme (GPS) developed by Liu [International Journal of Non-Linear Mechanics 36 (2001) 1047–1068] to atimestep-sizeadaptivescheme, xℓ+1=xℓ+hf(xℓ,tℓ), where x∈Rn is the system variables we are concerned with, and f(x,t)∈Rn is atime-varying vector field. The scheme has the form similar to the Euler scheme, xℓ+1=xℓ+Δtf(xℓ,tℓ), but our step-sizeh is adaptive automatically. Very interestingly, the ratio h/Δt, which we call the adaptive factor, can forecast the appearance of chaos if the considered dynamical system becomes chaotical. The numerical examples of the Duffing equation, the Lorenz equation and the Rossler equation, which may exhibit chaotic behaviors under certain parameters values, are used to demonstrate these phenomena. Two other non-chaotic examples are included to compare the performance of the GPS and the adaptive one.
Relation: 299(4-5), pp.977-989
URI: http://ntour.ntou.edu.tw/handle/987654321/24433
Appears in Collections:[系統工程暨造船學系] 期刊論文

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