Computation of 2D Manifold Based on Generalized Condition

Zhong Wu; Meng Jia; Qing Hua Ji

doi:10.4028/www.scientific.net/AMR.580.210

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 580Computation of 2D Manifold Based on Generalized...

Computation of 2D Manifold Based on Generalized Condition

Abstract:

The new algorithm uses the idea of growing the manifold. The preimage of the new point is found quickly with a method called gradient prediction scheme and a new accuracy criterion is proposed. Furthermore, our algorithm is capable of computing both stable and unstable one dimensional manifold.

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Periodical:

Advanced Materials Research (Volume 580)

Pages:

210-213

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.580.210

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Online since:

October 2012

Authors:

Zhong Wu, Meng Jia, Qing Hua Ji

Keywords:

Derivative Transportation, Dynamical System, Map

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References

[1] Z. You, E. J. Kostelich, J. A. Yorke, Calculating stable and unstable manifolds, Int. J. Bifurc. Chaos Appl. Sci. Eng. 1(1991) p.605.

DOI: 10.1142/s0218127491000440

Google Scholar

[2] T. S. Parker, L. O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer, Berlin, (1989).

Google Scholar

[3] D. Hobson, An efficient method for computing invariant manifolds, J. Comput. Phys. 104(1991) p.14.

Google Scholar

[4] B. Krauskopf, H. M. Osinga, Growing unstable manifolds of planar maps, 1517, 1997, http: /www. ima. umn. edu/preprints/OCT97/1517. ps. gz.

Google Scholar

[5] B. Krauskopf, H. M. Osinga, Growing 1D and quasi-2D unstable manifolds of maps, J. Comput. Phys, 146(1998) p.404.

DOI: 10.1006/jcph.1998.6059

Google Scholar

[6] J. P. England, B. Krauskopf, and H. M. Osinga, Computing One-Dimensional Stable Manifolds and Stable Sets of Planar Maps without the Inverse, SIAM J. Appl. Dyn. Syst. 3(2004) p.161.

DOI: 10.1137/030600131

Google Scholar

[7] M. Dellnitz, A. Hohmann, A subdivision algorithm for the computation of unstable manifolds and global attractors, Numer. Math. 75(1997) p.293.

DOI: 10.1007/s002110050240

Google Scholar

[8] J. Palis, W. D. Melo. Geometric Theory of Dynamical Systems. Springer-Verlag, New York, (1982).

Google Scholar

[9] W. Govaerts, Khoshsiar R. Ghaziani, Yu. A. Kuznetsov and H. G. E. Meijer, Cl MatContM: A toolbox for continuation and bifurcation of cycles of maps, (2006) http: /www. matcont. UGent. be.

Google Scholar

[10] R. Khoshsiar Ghaziani, W. Govaerts, Yu. A. Kuznetsov and H. G. E. Meijer, Numerical continuation of connecting orbits of maps in MATLAB, J. Diff. Eqns. Appl. 15(2009) p.849.

DOI: 10.1080/10236190802357677

Google Scholar