A nine-dimensional lorenz system to study high-dimensional chaos

Journal of Physics A: Mathematical and General

Volumn 31, Issue 34, 1998, Pages 7121-7139

  Reiterer, Peter ^a   Lainscsek, Claudia ^a   Schürrer, Ferdinand ^a   Letellier, Christophe ^b   Maquet, Jean ^b  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITÉ DE ROUEN   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038931082     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/34/015     Document Type: Article

References (34)

1. Lorenz E N 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130-41
2. Packard N H, Crutchfield J P, Farmer J D and Shaw R S 1980 Geometry from a time series Phys. Rev. Lett. 45 712-16
3. Takens F 1981 Detecting strange attractors in turbulence Dynamical Systems and Turbulence (Lecture Notes in Mathematics 898) ed D A Rand and L S Young (Berlin: Springer) pp 366-81
4. Grassberger P and Proccacia I 1983 Measuring the strangeness of strange attractors Physica 9D 189-208
5. Eckmann J P, Oliffson S, Ruelle D and Ciliberto S 1986 Lyapunov exponents from time series Phys. Rev. A 34 4971-9
6. Abarbanel H D I, Brown R, Sidorowich J J and Tsimring L Sh 1993 The analysis of observed chaotic data in physical systems Rev. Mod. Phys. 65 1331-88
7. Abarbanel H D I 1995 Analysing and utilizing time series observations from chaotic systems Nonlinearity and Chaos Engineering Dynamics ed J M T Thompson and S R Bishop (New York: Wiley) pp 379-91
8. Metropolis N, Stein M L and Stein P R 1973 On finite limit sets for transformations on the unit interval J. Comb. Theor. A 15 25-44
9. Collet P and Eckmann J P 1980 Iterated Maps on the Interval as Dynamical Systems (Progress in Physics) ed A Jaffe and D Ruelle (Boston, MA: Birkhäuser)
10. Hall T 1994 The creation of horseshoes Nonlinearity 7 861-924
11. Mindlin G B, Hou X J, Solari H G, Gilmore R and Tufillaro N B 1990 Classification of strange attractors by integers Phys. Rev. Lett. 64 2350-3
12. Mindlin G B, Solari H G, Natiello M A, Gilmore R and Hou X J 1991 Topological analysis of chaotic time series data from the Belousov-Zhabotinski reaction J. Nonlin. Sci. 1 147-73
13. Tufillaro N B, Abbott T and Reilly J 1992 An Experimental Approach to Nonlinear Dynamics and Chaos (New York: Addison-Wesley)
14. Rössler O E 1979 An equation for hyperchaos Phys. Lett. 71A 155-7
15. Rössler O E 1976 An equation for continuous chaos Phys. Lett. 57A 397-8
16. Cordon R P and Velarde M G 1975 On the (nonlinear) foundations of Boussinesq approximation applicable to a thin layer of fluid J. Physique 36 591-601
17. Normand C and Pomeau Y 1977 Convective instability: a physicist's approach Rev. Mod. Phys. 49 581-624
18. Palm E 1975 Nonlinear thermal convection Annu. Rev. Fluid Mech. 7 39-61
19. Lord Rayleigh 1916 On convection currents in a horizontal layer of fluid when the higher temperature is on the under side Phil. Mag. 32 529-46
20. Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon)
21. Koschmieder E L 1993 Bénard Cells and Taylor Vortices (Cambridge: Cambridge University Press)
22. Benettin G, Galgani L, Giorgilli A and Strelcyn J M 1980 Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them Meccanica 15 9-30
23. Feigenbaum M J 1978 Quantitative universality for a class of nonlinear transformation J. Stat. Phys. 19 25-52
24. Coullet P and Tresser C 1978 Itérations d'endomorphismes et groupe de renormalisation J. Physique 8 C5-25
25. Letellier C, Dutertre P and Maheu B 1995 Unstable periodic orbits and templates of the Rössler system: toward a systematic topological characterization Chaos 5 271-82
26. Letellier C, Le Sceller L, Dutertre P, Gouesbet G, Fei Z and Hudson J L 1995 Topological characterization and global vector field reconstruction from an experimental electrochemical system J. Phys. Chem. 99 7016-27
27. Franceschini V and Tebaldi C 1979 Sequences of infinites bifurcations and turbulence in five-mode truncation of the Navier-Stokes equations J. Stat. Phys. 21 707
28. Press W H, Flannery B P, Teukolsky S A and Vetterling W T 1995 Numerical Recipes in C (Cambridge: Cambridge University Press)
29. Mindlin G B and Solari H G 1997 Tori and Klein bottles in four-dimensional chaotic flows Physica 102D 177-86
30. Birman J S and Williams R F 1983 Knotted periodic orbits in dynamical systems: Lorenz's equations Topology 22 47-82
31. Melvin P and Tufillaro N B 1991 Templates and framed braids Phys. Rev. A 44 3419-22
32. Tufillaro N B, Wyckoff P, Brown R, Schreiber T and Molteno T 1995 Topological time series analysis of a string experiment and its synchronized model Phys. Rev. E 51 164-74
33. Le Sceller L, Letellier C and Gouesbet G 1994 Algebraic evaluation of linking numbers of unstable periodic orbits in chaotic attractors Phys. Rev. E 49 4693-5
34. 2-approximation on nets Phys. Rev. E 49 4955-72