Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit

Physical Review Letters

Volumn 101, Issue 5, 2008, Pages

  Bonatto, Cristian ^a   Gallas, Jason A C ^a  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRON TUBES; PHASE DIAGRAMS;

FOCAL POINTS; NONLINEAR RESISTANCE; RESISTIVE CIRCUITS;

NETWORKS (CIRCUITS);

EID: 49149128642     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.101.054101     Document Type: Article

References (36)

1. Handbook of Chaos Control, edited by, E. Schöll, and, H.G. Schuster, (Wiley-VCH, Weinheim, 2007).
2. J. Argyris, G. Faust, and M. Haase, Die Erforschung des Chaos, Zweite Auflage (Springer, Berlin, 2008), 2nd ed.
3. M.J. Ogorzalek, Chaos and Complexity in Nonlinear Electronic Circuits (World Scientific, Singapore, 1997).
4. Digital Communications Using Chaos and Nonlinear Dynamics, edited by, L.E. Larson, J.-M. Liu, and, L.S. Tsimrig, (Springer, New York, 2006).
5. R.J. Field and L. Györgyi, Chaos in Chemistry and Biochemistry (World Scientific, Singapore, 1993).
6. For a tutorial, see C.P. Silva, IEEE Trans. Circuit Syst. ICSYBT 0098-4094 40, 675 (1993);
7. see also J.D. Meiss, Differential Dynamical Systems (SIAM, Philadelphia, 2007).
8. S. Wiggins, Global Bifurcations and Chaos (Springer, New York, 1988).
9. Y.A. Kusnetzov, Elements of Applied Bifurcation Theory (Springer, New York, 1998).
10. P. Glendinning, Stability, Instability and Chaos (Cambridge University Press, Cambridge, England, 1994);
11. P. Glendinning and C. Sparrow, J. Stat. Phys. 35, 645 (1984). JSTPSB 0022-4715 10.1007/BF01010828
12. G. Nicolis, Introduction to Nonlinear Science (Cambridge University Press, Cambridge, England, 1995);
13. P. Gaspard, R. Kapral, and G. Nicolis, J. Stat. Phys. 35, 697 (1984). JSTPSB 0022-4715 10.1007/BF01010829
14. B. Fiedler, in Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability, edited by, G. Dangelmayr, B. Fiedler, K. Kirchgässner, and, A. Mielke, (Longman, Essex, 1996), Chap..
15. Y. Nishio, N. Inaba, S. Mori, and T. Saito, IEEE Trans. Circuit Syst. ICSYBT 0098-4094 37, 473 (1990). 10.1109/31.52750
16. J.A.C. Gallas, Phys. Rev. Lett. 70, 2714 (1993); PRLTAO 0031-9007 10.1103/PhysRevLett.70.2714
17. J.A.C. Gallas Physica (Amsterdam) 89D, 71 (1995); PDNPDT 0167-2789 10.1016/0167-2789(95)00215-4
18. J.A.C. Gallas Physica (Amsterdam) 202A, 196 (1994); PHYADX 0378-4371 10.1016/0378-4371(94)90174-0
19. J.A.C. Gallas Appl. Phys. B APBOEM 0946-2171 60, S-203 (1995).
20. The previous two references introduce the canonical shrimp generator: xt+1=a-(b-xt2)2;
21. see also Hunt, Physica (Amsterdam) 129D, 35 (1999). PDNPDT 0167-2789 10.1016/S0167-2789(98)00201-2
22. C. Bonatto, J.C. Garreau, and J.A.C. Gallas, Phys. Rev. Lett. 95, 143905 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.143905
23. C. Bonatto and J.A.C. Gallas, Phys. Rev. E 75, 055204(R) (2007); PLEEE8 1063-651X 10.1103/PhysRevE.75.055204
24. C. Bonatto J.A.C. Gallas Phil. Trans. R. Soc. A PTRMAD 1364-503X 366, 505 (2008); 10.1098/rsta.2007.2107
25. C. Bonatto, J.A.C. Gallas, and Y. Ueda, Phys. Rev. E 77, 026217 (2008). PLEEE8 1063-651X 10.1103/PhysRevE.77.026217
26. F. Argoul, J. Chim. Phys. 84, 1367 (1987). JCPBAN 0021-7689
27. D. Hennequin, Phys. Rev. A 37, 2243 (1988); PLRAAN 1050-2947 10.1103/PhysRevA.37.2243
28. D. Dangoisse, Europhys. Lett. 6, 335 (1988); EULEEJ 0295-5075 10.1209/0295-5075/6/4/010
29. F.T. Arecchi, Europhys. Lett. 6, 677 (1988); EULEEJ 0295-5075 10.1209/0295-5075/6/8/002
30. A. Zeni, Phys. Lett. A 172, 247 (1993). PYLAAG 0375-9601 10.1016/0375-9601(93)91016-X
31. T. Braun, J.A. Lisboa, and J.A.C. Gallas, Phys. Rev. Lett. 68, 2770 (1992). PRLTAO 0031-9007 10.1103/PhysRevLett.68.2770
32. A. Sensse, M.J.B. Hauser, and M. Eiswirth, J. Chem. Phys. 125, 014901 (2006). JCPSA6 0021-9606 10.1063/1.2207140
33. S. Takesue and K. Kaneko, Prog. Theor. Phys. PTPKAV 0033-068X 71, 35 (1984); 10.1143/PTP.71.35
34. H.E. Nusse and J.A. Yorke, Science 271, 1376 (1996); SCIEAS 0036-8075 10.1126/science.271.5254.1376
35. J. Aguirre and M. Sanjuan, Physica (Amsterdam) 171D, 41 (2002); PDNPDT 0167-2789 10.1016/S0167-2789(02)00565-1
36. Z. Hai-Lin, Chinese Phys. B 1674-1056 17, 117 (2008). 10.1088/1674-1056/17/1/021