Abstract
By using the fact that Jacobian transports derivative along the orbit of the invariant manifold, a new algorithm for computing 1D manifold is proposed first. The new mesh point is located with a Prediction-Correction scheme which reduces the searching time and at the same time gives rise to a simplified accuracy condition. Two dimensional manifold is computed by covering it with orbits of 1D sub-manifold. A generalized Foliation Condition is used to guarantee that the 2D manifold is growing uniformly along the orbits of 1D sub-manifold in different directions. The performance of the algorithm is demonstrated with hyper chaotic 3D Hénon map and Lorenz system.
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Acknowledgments
The work is supported by Tackle Key Problems in Science and Technology of The Nan province in China (Grant No. 112102210014), Tackle Key Problems in Science and Technology of **nxiang city in China (Grant No. ZG11009).
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© 2013 Springer-Verlag London
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Wu, Z., Jia, M., Ji, Q. (2013). Compute 2D Stable and Unstable Manifolds of Nonlinear Maps. In: Du, W. (eds) Informatics and Management Science III. Lecture Notes in Electrical Engineering, vol 206. Springer, London. https://doi.org/10.1007/978-1-4471-4790-9_86
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DOI: https://doi.org/10.1007/978-1-4471-4790-9_86
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