Intermingled basins in coupled Lorenz systems

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

Volumn 85, Issue 3, 2012, Pages

  Camargo, Sabrina ^a   Viana, Ricardo L ^b   Anteneodo, Celia ^a,c  

^a PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^c NATIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY FOR COMPLEX SYSTEMS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

ANTI-SYNCHRONIZATION; BASINS OF ATTRACTION; CHAOTIC MOTIONS; COUPLED LORENZ SYSTEMS; COUPLING STRENGTHS; GLOBAL SYNCHRONIZATION; LORENZ OSCILLATORS; MATHEMATICAL REQUIREMENTS;

CONDENSED MATTER PHYSICS;

PHYSICS;

EID: 84859040429     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.036207     Document Type: Article

References (39)

1. E. N. Lorenz, J. Atmosph. Sci. JAHSAK 0022-4928 10.1175/1520-0469(1963) 020<0130:DNF>2.0.CO;2 20, 130 (1963).
2. H. Haken, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(75)90353-9 53, 77 (1975).
3. E. Knobloch, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(81)90274-7 82, 439 (1981);
4. I. M. Moroz, Proc. R. Soc. A 1364-5021 10.1098/rspa.2011.0216 468, 288 (2012).
5. H. Fujisaka and T. Yamada, Progr. Theoret. Phys. PTPKAV 0033-068X 10.1143/PTP.69.32 69, 32 (1983);
6. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.821 64, 821 (1990).
7. A. Pikowsky, M. Rosenblum, and J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2003).
8. K. M. Cuomo and A. V. Oppenheim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.65 71, 65 (1993);
9. M. Sushchik, N. Rulkov, L. Larson, L. Tsimrin, H. Abarbanel, K. Yao, and A. Volkovskii, Comm. Lett. IEEE 1089-7798 10.1109/4234.841319 4, 128 (2000).
10. J. Aguirre, R. L. Viana, and M. A. F. Sanjuán, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.333 81, 333 (2009).
11. C. Grebogi, E. Ott, and J. A. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(83)90126-4 7, 181 (1983).
12. J. C. Alexander, J. A. Yorke, Z. You, and I. Kan, Int. J. Bifur. Chaos IJBEE4 0218-1274 10.1142/S0218127492000446 2, 795 (1992).
13. E. Ott, J. C. Sommerer, J. C. Alexander, I. Kan, and J. A. Yorke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.4134 71, 4134 (1993).
14. E. Ott and J. C. Sommerer, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(94)90114-7 188, 39 (1994).
15. Y.-C. Lai and C. Grebogi, Phys. Rev. E 1539-3755 10.1103/PhysRevE.52. R3313 52, R3313 (1995).
16. Y.-C. Lai, C. Grebogi, J. A. Yorke, and S. C. Venkataramani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.55 77, 55 (1996).
17. An attractor is the limit set of orbits from a set of initial conditions whose volume in phase-space is non-null. J. Milnor, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01212280 99, 177 (1985).
18. S. Yanchuk, Y. Maistrenko, and E. Mosekilde, Chaos CHAOEH 1054-1500 10.1063/1.1496536 13, 388 (2003). (Pubitemid 36419936)
19. P. Ashwin, J. Buescu, and I. N. Stewart, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(94)90947-4 193, 126 (1994).
20. S. Yanchuk, Y. Maintrenko, and E. Mosekilde, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(01)00221-4 154, 26 (2001); (Pubitemid 32572559)
21. S. Yanchuk, Y. Maistrenko, B. Lading, and E. Mosekilde, Int. J. Bifurc. Chaos 0218-1274 10.1142/S0218127400001584 10, 2629 (2000).
22. Yu. L. Maistrenko, V. L. Maistrenko, A. Popovich, and E. Mosekilde, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.57.2713 57, 2713 (1998).
23. J. C. Sommerer, Johns Hopkins APL Tech. Dig. 16, 333 (1995).
24. R. F. Pereira, S. Camargo, S. E. de S. Pinto, S. R. Lopes, and R. L. Viana, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.056214 78, 056214 (2008).
25. C.-M. Kim, S. Rim, W.-K. Kye, J.-W. Ryu, and Y.-J. Park, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2003.10.051 320, 39 (2003).
26. M. C. Vergés, R. F. Pereira, S. R. Lopes, R. L. Viana, and T. Kapitaniak, Physica A PHYADX 0378-4371 10.1016/j.physa.2009.02.015 388, 2515 (2009).
27. E. Ott, J. C. Alexander, I. Kan, J. C. Sommerer, and J. A. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90047-7 76, 384 (1994).
28. R. Karnatak, R. Ramaswamy, and A. Prasad, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.035201 76, 035201 (2007). (Pubitemid 47443095)
29. H. E. Nusse and J. A. Yorke, Science SCIEAS 0036-8075 10.1126/science.271.5254.1376 271, 1376 (1996).
30. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Physica D PDNPDT 0167-2789 10.1016/0167-2789(85)90011-9 16, 285 (1985).
31. J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.52.R1253 52, R1253 (1995).
32. D. Viswanath, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/16/3/314 16, 1035 (2003);
33. V. Franceschini, C. Giberti, and Z. Zhengi, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/6/2/006 6, 251 (1993);
34. Z. Galias and W. Tucker, Proc. IEEE Int. Symposium on Circuits and Systems, ISCAS'08, 764 (2008).
35. A. Trevisan and F. Pancotti, J. Atmos. Sci. JAHSAK 0022-4928 10.1175/1520-0469(1998)055<0390:POLVAS>2.0.CO;2 55, 390 (1997).
36. Y.-C. Lai and V. Andrade, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.056228 64, 056228 (2001).
37. S. Camargo, S. R. Lopes, and R. L. Viana, J. Phys. Conf. Series 1742-6588 10.1088/1742-6596/246/1/012001 246, 012001 (2010).
38. C. Grebogi, S. W. McDonald, E. Ott, and J. A. Yorke, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(85)90220-8 100, 1 (1985).
39. S. W. McDonald, C. Grebogi, E. Ott, and J. A. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(85)90001-6 17, 125 (1985).