n-Dimensional stable and unstable manifolds of hyperbolic singular point

Chaos, Solitons and Fractals

Volumn 29, Issue 5, 2006, Pages 1155-1164

  Yanhui, Li ^a   Siming, Zhu ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; FRACTALS; ORBITS; SOLITONS;

DYNAMICAL SYSTEMS; HYPERBOLIC SINGULAR POINT; STABLE AND UNSTABLE MANIFOLDS;

NUMERICAL METHODS;

EID: 33645859329     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.08.129     Document Type: Article

References (22)

1. Krauskopf B., and Osinga H. Two-dimensional global manifolds of vector fields. Chaos, Solitons & Fractals 3 (1999) 768-774
2. Wolf J.B., and Winfried K. Numerical Taylor expansions of invariant manifolds in large dynamical systems. Numer Math 80 (1998) 1-38
3. Vakakis A.F., and Azeez M.F.A. Analytic approximation of the homoclinic orbits of the Lorenz system at σ = 10, b = 8/3 and ρ = 13.926.... Nonlin Dyn 15 (1998) 245-257
4. Broer H.W., Osinga1 H.M., and Vegter G. Algorithms for computing normally hyperbolic invariant manifolds. Zeitschr Angew Math Phys ZAMP 48 (1997) 480-524
5. Palis J., and Takens F. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations. Cambridge studies in advanced mathematics vol. 35 (1993), Cambridge University Press
6. Ruelle D. Elements of dicerentiable dynamics and bifurcation theory (1989), Academic Press, New York
7. Shub M. Global stability of dynamical systems (1987), Springer-Verlag
8. Sandstede B. Convergence estimates for the numerical approximation of homoclinic solutions. IMA J Numer Anal 17 (1997) 437-462
9. Beyn W.J. The numerical computation of connecting orbits in dynamical systems. IMA J Numer Anal 9 (1990) 379-405
10. Friedman M.J., and Doedel E.J. Numerical computation and continuation of invariant manifolds connecting fixed points. IMA J Numer Anal 28 (1991) 789-808
11. Leonov G.A. Bounds for attractors and the existence of homoclinic orbits in the Lorenz system. PMM J Appl Math Mecn 65 (2001) 19-32
12. Li Z., Chen G., and Wolfgang A.H. Homoclinic and heteroclinic orbits in a modified Lorenz system. Inform Sci 165 (2004) 235-245
13. Spreuer H., and Adams E. On the strange attractor and transverse homoclinic orbits for the Lorenz equations. J Math Anal Appl 190 (1995) 329-360
14. Spreuer H., Adams E., and Karlsruhe. On the existence and the verified determination of homoclinic and heteroclinic orbits of the origin for the Lorenz equation. Comput Suppl 9 (1993) 233-246
15. Meyer K.R. The evolution of the stable and unstable manifold of an equilibrium point. Celest Mech Dyn Astron 70 (1998) 159-165
16. Lassoued L., and Mathlouthi S. A numerical method for finding homoclinic orbits of Hamiltonian systems. Numer Funct Anal Optim 13 (1992) 155-172
17. Schecter S. Rate of convergence of numerical approximations to homoclinic bifurcation points. IMA J Numer Anal 15 (1995) 23-60
18. Champneys A.R., Kuznetsov Yu.A., and Sandstede B. A numerical toolbox for homoclinic bifurcation analysis. Int J Bifurcat Chaos 6 (1996) 867-887
19. Bai F., and Champneys A.R. Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two. Dyn Stab Syst 11 (1996) 325-346
20. Krauskopf B., and Osinga H. Two-dimensional global manifolds of vector fields. Chaos, Solitons & Fractals 9 (1999) 768-774
21. Morozov A.D., and Dragunova T.N. Visualization and analysis of invariant sets of dynamical systems. Nonlin Anal Theory 47 (2001) 5285-5296
22. Qin Y. Teaching materials about ordinary question of motion stabilization (1958), Science Publishing Company, Beijing (in Chinese)