Experimental observation of a complex periodic window

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 3, 2008, Pages

  Maranhao D M ^a   Baptista, M S ^b   Sartorelli, J C ^a   Caldas, I L ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; LARGE SCALE SYSTEMS; NUMERICAL METHODS; PARAMETER ESTIMATION; PROBLEM SOLVING;

CHUA'S CIRCUIT; COMPLEX PERIODIC WINDOW; PARAMETER VALUES; TWO-DIMENSIONAL PARAMETER SPACE;

TIME VARYING SYSTEMS;

EID: 41549157822     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.037202     Document Type: Article

References (19)

1. M. V. Jakobson, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01941800 81, 39 (1981).
2. J. Graczyk and G. wiatek, Ann. Math. ANMAAH 0003-486X 10.2307/2951831 146, 1 (1997).
3. Since the parameter interval occupied by higher-period attractors decreases in a power-law fashion with the period of the attractor, we do not expect to observe the higher-period attractors of a PW in an experiment. In this work, we only consider the lowest-period periodic attractor in a PW.
4. M. S. Baptista, E. E. Macau, C. Grebogi, Y.-C. Lai, and E. Rosa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.4835 62, 4835 (2000).
5. J. A. C. Gallas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 70.2714 70, 2714 (1993).
6. B. Hunt and E. Ott, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/30/20/ 012 30, 7067 (1997).
7. E. Barreto, B. R. Hunt, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.4561 78, 4561 (1997).
8. M. S. Baptista, E. Barreto, and C. Grebogi, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127403008181 13, 2681 (2003).
9. M. S. Baptista and I. L. Caldas, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/0960-0779(95)00083-6 7, 325 (1996).
10. C. Bonatto, J. C. Garreau, and J. A. C. Gallas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.143905 95, 143905 (2005)
11. Y. Zou, M. Thiel, M. C. Romano, Q. Bi, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127406016987 16, 3567 (2006)
12. V. Castro, M. Monti, W. B. Pardo, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127407017689 17, 965 (2007).
13. M. S. Baptista, Ph.D. thesis, University of São Paulo, 1996, Chap. 5, p. 100, http://www.teses.usp.br
14. F. Takens, in Dynamical Systems and Turbulence, edited by, D. A. Rand, and, L. S. Young, Springer Lectures Notes in Mathematics, Vol. 898 (Springer-Verlag, Berlin, 1980).
15. R. Gilmore and J. W. L. McCallum, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.935 51, 935 (1995).
16. N. Metropolis, M. L. Stein, and P. R. Stein, J. Comb. Theory, Ser. A JCBTA7 0097-3165 10.1016/0097-3165(73)90033-2 15, 25 (1973).
17. A Shilnikov homoclinic orbit is an orbit homoclinic to a saddle-focus point for which | ρ/λ | <1, where λ is one real eigenvalue and ρ is the real part of the other two complex-conjugate eigenvalues.
18. P. Gaspard, R. Kapral, and G. Nicolis, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01010829 35, 697 (1984).
19. R. O. Medrano-T., M. S. Baptista, and I. L. Caldas, Chaos CHAOEH 1054-1500 10.1063/1.2401060 16, 043119 (2006).