A Gradient-Prediction Algorithm for Computing One Dimensional Stable and Unstable Manifolds of Maps

Meng Jia; Yi Ru; Jun Jie Xi; Qing Hua Ji; Zhong Wu

doi:10.4028/www.scientific.net/AMR.580.78

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 580A Gradient-Prediction Algorithm for Computing One...

A Gradient-Prediction Algorithm for Computing One Dimensional Stable and Unstable Manifolds of Maps

Abstract:

A new algorithm is presented to compute both one dimensional stable and unstable manifolds of planar maps. The global manifold is grown from a local manifold and one point is added each step. It is proved that the gradient of the global manifold can be predicted by the known points on the manifold with a gradient prediction scheme and it can be used to locate the image or preimage of the new point quickly. A new accuracy criterion is derived from the gradient prediction scheme. The performance of the algorithm is tested with several well-known examples.

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Periodical:

Advanced Materials Research (Volume 580)

Pages:

78-81

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.580.78

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Online since:

October 2012

Authors:

Meng Jia, Yi Ru, Jun Jie Xi, Qing Hua Ji, Zhong Wu

Keywords:

Discrete Dynamical System, Gradient Prediction, Hyperbolic Fixed Point, Stable Manifold, Taylor Series, Unstable Manifold

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