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Intelligent Engineering Systems through Artificial Neural Networks

Editor
Cihan H. Dagli
Cihan H. Dagli
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K. Mark Bryden
K. Mark Bryden
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Steven M. Corns
Steven M. Corns
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Mitsuo Gen
Mitsuo Gen
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Kagan Tumer
Kagan Tumer
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Gürsel Süer
Gürsel Süer
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ISBN:
9780791802953
No. of Pages:
636
Publisher:
ASME Press
Publication date:
2009

This paper compares the Lyapunov exponents spectrum computation utilizing group theoretical representations of orthogonal matrices applied to decompositions of the tangent map with the Gram-Schmidt Reorthonormalization method. Former method formulates an initial value problem for a system of differential equations and numerically solves them to obtain the Lyapunov exponents. A consequence of this method is the separation between the exponents and the angles pieces in the evolution equations. To illustrate the application of these methods to 2-dim and 3-dim systems, we turn to the standard test case of driven dissipative oscillator in periodic potential and the Lorenz equations. Some experimental observations are given for these systems.

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