Topological analysis of chaos in equivariant electronic circuits

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 12 A/B, 1996, Pages 2531-2555

  Letellier, C ^a   Gouesbet, G ^a   Rulkov, N F ^b  

^a CNRS   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008158353     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0218127496001624     Document Type: Article

References (38)

1. Agarwal, A. K., Ahalpara, D. P., Kaw, P. K., Prablakera, H. R. & Sen, A. [1990] "Model equations from a chaotic time series," J. of Phys. 35(3), 287-301.
2. Belyakov, L. [1984] "Bifurcation of the system with homoclinic curve of a saddle-focus with saddle quantity zero," Math. Zam. 36, 838-843.
3. Breeden, J. L. & Hübler, A. [1990] "Reconstructing equations of motion from experimental data with hidden variables," Phys. Rev. A42(10), 5817-5826.
4. Brown, R., Rulkov, N. F. & Tracy, E. R. [1995] "Modeling and synchronizing chaotic systems from time-series data," Phys. Rev. E49(5), 3784-3800.
5. Casdagli, M., Eubank, S., Farmer, J. D. & Gibson, J. [1991] "State space reconstruction with noise," Physica D51, 52-98.
6. Chua, L. O. [1992] "The genesis of Chua's circuit," Archiv fur Elektronic und Ubertragungstechnik 46, 250-257.
7. Crutchfield, J. P. & McNamara, B. S. [1987] "Equations of motion from a data series," Complex Systems 1, 417-452.
8. Duan, B., Wang, Y. & Zhao, H. [1994] "Symbolic dynamics for the sin map," Commun. Theor. Phys. 22, 299-306.
9. Dutertre, P. [1995] Caractérization des attracteurs étranges par la population d'orbites périodiques Ph'D dissertation, URA CNRS 230, LESP, Rouen, France.
10. Fa-Geng Xie. [1994] "Symbolic dynamics for the general quartic map," Commun. Theor. Phys. 22, 43-52.
11. Fang, H. P. [1994] "Dynamics of strongly dissipative systems," Phys. Rev. E49(6), 5025-5031.
12. Farmer, J. D. & Sidorowitch, J. J. [1987] "Predicting chaotic time series," Phys. Rev. Lett. 59, 845-848.
13. Fraser, A. M. & Swinney, H. L. [1986] "Independent coordinates for strange attractors from mutual information," Phys. Rev. A33(2), 1134-1140.
14. Gibson, J. F., Farmer, J. D., Casdagli, M. & Eubank, S. [1992] "An analytic approach to practical state space reconstruction," Physica D57, 1-30.
15. Giona, M., Lendini, F. & Cimagalli, V. [1991] "Functional reconstruction and local prediction of chaotic time series," Phys. Rev. A44(6), 3496-3502.
16. Glendining, P. & Sparrow, C. [1991] "Local and global behavior near homoclinc orbits," J. Stat. Phys. 35, 645-696.
17. Gouesbet, G. & Maquet, J. [1992] "Construction of phenomenological models from numerical scalar time series," Physica D58, 202-215.
18. 2-approximation on nets," Phys. Rev. E49(6), 4955-4972.
19. Grassberger, P. & Proccacia, I. [1983] "Measuring the strangeness of strange attractors," Physica D9, 189-208.
20. Kennel, M. B., Brown, R. & Abarbanel, H. D. I. [1992] "Determining embedding dimension for phase-space reconstruction using a geometrical construction," Phys. Rev. A45, 3403-3411.
21. King, G. P. & Stewart, I. [1992] "Phase space reconstruction for symmetric dynamical systems," Physica D58, 216-228.
22. Kocarev, L., Tasev, Z., Dimovski, D. & Chua, L. O. [1994] "Knotted periodic orbits in Chua's circuit," Int. J. Bifurcation Chaos 4(3), 609-621.
23. Kocarev, L., Tasev, Z. & Dimovski, D. [1994] "Topological description of a chaotic attractor with spiral structure," Phys. Lett. A190, 399-402.
24. Letellier, C., Dutertre, P. & Gouesbet, G. [1994] "Characterization of the Lorenz system taking into account the equivariance of the vector field," Phys. Rev. E49(4), 3492-3495.
25. Letellier, C., Le Sceller, L., Maréchal, E., Dutertre, P., Maheu, B., Gouesbet, G., Fei, Z. & Hudson, J. L. [1995] "Global vector field reconstruction from a chaotic experimental signal in copper electrodissolution," Phys. Rev. E51(5), 4262-4266.
26. Letellier, C., Le Sceller, L., Dutertre, P., Gouesbet, G., Fei, Z. & Hudson, J. L. [1995] "Topological characterization and global vector field reconstruction from experimental electrochemical system," J. Phys. Chem. 99, 7016-7027.
27. Letellier, C., Dutertre, P., Reizner, J. & Gouesbet, G. [1996] "Evolution of a multimodal map induced by an equivariant vector field," J. Phys A29, 5359-5375.
28. Letellier, C. & Gouesbet, G. [1996] "Topological characterization of reconstructed attractors modeling out symmetries," J. Phys. II 6, 1615-1638.
29. Lorenz, E. N. [1963] "Deterministic Nonperiodic Flow," J. of the Atm. Sci. 20, 130-141.
30. Melvin, P. & Tufillaro, N. B. [1991] "Templates and framed braids," Phys. Rev. A44 (6), 3419-3422.
31. Mindlin, G. B. & Solari, H. G. [1995] "Topologically inequivalent embeddings," Phys. Rev. E52(2), 1497-1502.
32. Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw, R. S. [1980] "Geometry from a time series," Phys. Rev. Lett. 45(9), 712-716.
33. Palus, M. & Dvoràck, I. [1992] "Singular-value decomposition in attractor reconstruction. Pitfalls and precautions," Physica D55, 221-234.
34. Rulkov, N. F., Volkovski, A. R., Rodríguez-Lozano, A., Del Río, E. & Velarde, M. G. [1992] "Mutual information of chaotic self-oscillator with dissipative coupling," Int. J. Bifurcation and Chaos 2(3), 669-676.
35. Rulkov, N. F., Tsimring, L. S. & Abarbanel, H. D. I. [1994] "Tracking unstable orbits in chaos using dissipative feedback control," Phys. Rev. E50(1), 314-324.
36. Shilnikov, J. F. [1970] "A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type," Math. USSR Sbornik 10, 91-102.
37. Takens, F. [1981] "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence Lecture Notes in Mathematics 898, eds. Rand, D. A. & Young, L. S. (Springer-Verlag, New York), pp. 366-381.
38. Volkovski, A. R. & Rulkov, N. F. [1988] "Using one dimensional mapping for the experimental study of chaotic dynamics of a self-oscillator," Sov. Teck. Phys. Lett. 14, 656-659.