Construct 2D Stable and Unstable Manifolds of Nonlinear Maps

Peng Yao; Wei Zhang

doi:10.4028/www.scientific.net/AMR.580.432

Paper Titles

Parametric Design of Wind Turbine Blades Based on Pro/E
p.415

Experimental Study on Backlash Compensation of CNC Machine Tool
p.419

Shoe-Mounted Personal Navigation System Based on MEMS
p.423

Evolution of Pressure on Bearing's Surface in Dislocated Single Floating Ring Bearing
p.428

Construct 2D Stable and Unstable Manifolds of Nonlinear Maps
p.432

Dynamic Characteristics of Centrifugal Fan Impeller Based on Fluid-Solid Coupling
p.437

Experimental Research and Simulation in a Thermosyphon
p.441

Detection Devices and Technologies on Large-Scale Pipe Weld Surface Defect
p.445

Study on Photoelectric Performance of Organic Light Emitting Device
p.449

HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 580Construct 2D Stable and Unstable Manifolds of...

Construct 2D Stable and Unstable Manifolds of Nonlinear Maps

Abstract:

The procedure resolves the insertion of new mesh point, the searching of the image (or pre-image) and computation of the 1D sub-manifolds following the new mesh point tactfully, it does not require the 1D sub-manifolds to be computed from the initial circle and avoids the assembling of mesh points. The performance of the algorithm is demonstrated with hyper chaotic 3D Hénon map and Lorenz system.

You might also be interested in these eBooks

Mechanical Properties and Structural Materials

View Preview

Info:

Periodical:

Advanced Materials Research (Volume 580)

Pages:

432-436

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.580.432

Citation:

Cite this paper

Online since:

October 2012

Authors:

Peng Yao, Wei Zhang

Keywords:

3D Hénon Map, Chaotic Attractor, Lorenz System

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

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] 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

[6] 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

[7] D. Fundinger, Toward the Calculation of Higher-Dimensional Stable Manifolds and Stable Sets for Noninvertible and Piecewise-Smooth Maps. J Nonlinear Sci, 2008, 18, p.391.

DOI: 10.1007/s00332-007-9016-4

Google Scholar

[8] B. Krauskopf, H.M. Osinga, Globalizing two-dimensional unstable manifolds of maps. Int. J. Bifurc. Chaos Appl. Sci. Engrg., 1998, 8(3): p.483.

DOI: 10.1142/s0218127498000310

Google Scholar

[9] B. Krauskopf and H.M. Osinga, Two-dimensional global manifolds of vector fields. Chaos, 1999, 9(3): p.768.

DOI: 10.1063/1.166450

Google Scholar

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

Google Scholar

[11] S. V. Gonchenko, I. I. Ovsyannikov, C. Simo, D. Turaev, Three-dimensional Hénon-like maps and wild Lorenz-like attractors. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2005, 15(11): p.3493.

DOI: 10.1142/s0218127405014180

Google Scholar