Chua's circuit and the qualitative theory of dynamical systems

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 9, 1997, Pages 1911-1916

  Mira, Christian ^a  

^a INSA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038913351     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001497     Document Type: Article

References (25)

1. Afraimovitch, V. S., Bykov, V. V. & Shilnikov, L. P. [1983] "On the structurally unstable attracting limit sets of Lorenz type attractors," Trans. Mosc. Soc. 2, 153-215.
2. Afraimovitch, V. S. & Shilnikov, L. P. [1983] "Strange attractors and quasi attractors," in Nonlinear Dynamics and Turbulence, eds. Barenblatt, G. I. Ioss, G. & Joseph, D. D. (Pitman, Boston), pp. 1-34.
3. Afraïmovitch, V. S. & Shilnikov, L. P. [1991] "Invariant two-dimensional tori, their breakdown and stochasticity," Am. Math. Soc. Transl. 149(2), 201-211.
4. Andronov, A. A., Witt, A. A. & Khaïkin, S. E. [1966] Theory of Oscillators (Pergamon Press).
5. Andronov, A. A., Leontovich, E. A., Gordon, I. I. & Mayer, A. G. [1966a] "Qualitative theory of dynamic systems," in Russian (Ed. Nauka, Moscow).
6. Andronov, A. A., Leontovich, E. A., Gordon, I. I. & Mayer, A. G. [1967] "Bifurcation theory of dynamical systems in the plane," in Russian (Ed. Nauka, Moscow).
7. Chua, L. O. [1992] "The genesis of Chua's circuit," Archiv für Electronik und ubertragungstechnik 46, 250-257.
8. Chua, L. O. [1993] "Global unfolding of Chua's circuit," IEICE Trans. Fund. Electron. Commun. Comput. Sci. 76-SA, 704-734.
9. Chua, L. O. & Pivka, L. [1995] "Chaotic electronic circuits: Waves and spatio-temporal chaos," in Proc. Summer School in Automatic Control of Grenoble, Bifurcation, Chaos, Noninvertible Maps. Applications September 4-8.
10. Gonchenko, V. S., Turaev, D. V. & Shilnikov, L. P. [1992] "On models with a structurally unstable homoclinic Poincaré curve," Soviet Math. Dokl. 44(2), 422-425.
11. Gonchenko, V. S., Turaev, D. V. & Shilnikov, L. P. [1993a] "On models with a non-rough homoclinic Poincaré curve," Physica D62, 1-14.
12. Gonchenko, V. S., Turaev, D. V. & Shilnikov, L. P. [1993b] "On the existence of Newhouse regions near systems with a non-rough homoclinic Poincaré curve (multidimensional case)," Dokl. Rossiyskoi Akad. Nauk 329(4), 404-407.
13. Gonchenko, V. S. & Shilnikov, L. P. [1995] "On geometrical properties of two-dimensional diffeomorphisms with homoclinic tangencies," Int. J. Bifurcation and Chaos 5(3), 819-829.
14. Gonchenko, S. V., Turaev, D. V. & Shil'nikov, L. P. [1993] "Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve," Russian Acad. Sci. Dokl. Math. 47(3), 410-415.
15. Grebogi, C., Ott, E. & Yorke, J. A. [1983] "Fractal basin boundaries long-lived chaotic transients, and unstable-stable pair bifurcations," Phys. Rev. Lett. 50(13), 935-938.
16. Lozi, R. & Chua, L. O. [1993] "Secure communications via chaotic synchroniization," Int. J. Bifurcation and Chaos 3(1), 145-148.
17. Madan, R. N. [1993] "Chua's circuit: A paradigim for chaos," ed. Rabinder N. Madan. Nonlinear Science Series. Series B, Vol. 1. (World Scientific, Singapore).
18. Newhouse, S. E. [1974] "Diffeomorphisms with infinitely many sinks," Topology 13, 9-18.
19. Newhouse, S. E. [1979] "The abundance of of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms," Publ. Math. IHES 50, 101-151.
20. Shilnikov, L. P. [1967] "On a Poincaré-Birkhoff problem,́ Math. USSR Sborn. 3(3), 353-371.
21. Shilnikov, L. P. [1993] "Strange attractors and dynamical models," J. Circ. Syst. Comput. 3, 1-10.
22. Shilnikov, L. P. [1994] "Chua's circuit: Rigorous results and future problems," Int. J. Bifurcation and Chaos 4(3), 489-519.
23. Smale, S. [1963] "Diffeomorphisms with many periodic points," in Differential Combinatorial Topology, ed. Cairns S. S. (Princeton University Press), pp. 63-80.
24. Smale, S. [1966] "Structurally stable systems are not dense," Amer. J. Math. 88, 491-496.
25. Smale, S. [1967] "Differentiable dynamical systems," Bull Amer. Math. Soc. 73, 747-817.