Evaluation of dynamical models: Dissipative synchronization and other techniques

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

Volumn 74, Issue 6, 2006, Pages

  Aguirre, Luis Antonio ^a   Furtado, Edgar Campos ^a   Tôrres, Leonardo A B ^a  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATION THEORY; MATHEMATICAL MODELS; OSCILLATORS (ELECTRONIC); STATISTICAL METHODS; SYNCHRONIZATION;

BIFURCATION DIAGRAMS; COMPUTATIONAL COST; VAN DER POL OSCILLATORS;

NONLINEAR SYSTEMS;

EID: 33845574392     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.066203     Document Type: Article

References (80)

1. J. P. Crutchfield and B. S. McNamara, Complex Syst. CPSYEN 0891-2513 1, 417 (1987).
2. P. E. Rapp, T. I. Schmah, and A. I. Mees, Physica D PDNPDT 0167-2789 132, 133 (1999).
3. L. A. Aguirre and S. A. Billings, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 4, 109 (1994).
4. Y. V. Kolokolov and A. V. Monovskaya, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 16, 85 (2006).
5. T. P. Lim and Puthusserypady, Chaos CHAOEH 1054-1500 10.1063/1.2130927 16, 013106 (2006).
6. L. A. Aguirre, R. A. M. Lopes, G. Amaral, and C. Letellier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.026701 69, 026701 (2004).
7. L. A. Aguirre and E. M. Mendes, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127496000059 6, 279 (1996).
8. E. Bagarinao, K. Pakdaman, T. Nomura, and S. Sato, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.1073 60, 1073 (1999).
9. E. Bagarinao, K. Pakdaman, T. Nomura, and S. Sato, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00017-2 130, 211 (1999).
10. S. A. Billings and D. Coca, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127499000894 9, 1263 (1999).
11. J. H. B. Deane, Electron. Lett. ELLEAK 0013-5194 29, 957 (1993).
12. D. C. Hamil (unpublished).
13. H. M. Henrique, E. L. Lima, and J. C. Pinto, Lat. Am. Appl. Res. LAARE8 0327-0793 28, 187 (1998).
14. L. Le Sceller, C. Letellier, and G. Gouesbet, Phys. Lett. A PYLAAG 0375-9601 211, 211 (1996).
15. S. Ogawa, T. Ikeguuchi, T. Matozaki, and K. Aihara, IEICE Trans. Fundamentals IFESEX 0916-8508 E79-A, 1608 (1996).
16. C. Tao, Y. Zhang, G. Du, and J. J. Jiang, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.09.027 332, 197 (2004).
17. R. Bakker, J. C. Schouten, C. L. Giles, F. Takens, and C. M. van den Bleek, Neural Comput. NEUCEB 0899-7667 10.1162/089976600300014971 12, 2355 (2000).
18. M. Small and C. K. Tse, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.066701 66, 066701 (2002).
19. E. Bagarinao and S. Sato, Ann. Biomed. Eng. ABMECF 0090-6964 10.1114/1.1454134 30, 260 (2002).
20. B. P. Bezruchko and D. A. Smirnov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.016207 63, 016207 (2001).
21. A. Garulli, C. Mocenni, A. Vicino, and A. Tesi, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 13, 357 (2003).
22. G. Gouesbet and C. Letellier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.49.4955 49, 4955 (1994).
23. H. L. Hiew and C. P. Tsang, Inf. Sci. (N.Y.) ISIJBC 0020-0255 10.1016/0020-0255(94)90097-3 81, 193 (1994).
24. L. Jaeger and H. Kantz, Chaos CHAOEH 1054-1500 10.1063/1.166196 6, 440 (1996).
25. K. Judd and A. I. Mees, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(98) 00089-X 120, 273 (1998).
26. C. Letellier, L. Le Sceller, G. Gouesbet, F. Lusseyran, A. Kemoun, and B. Izrar, AIChE J. AICEAC 0001-1541 10.1002/aic.690430906 43, 2194 (1997).
27. U. Parlitz, Chaos CHAOEH 1054-1500 10.1063/1.1737818 14, 420 (2004).
28. P. Perona, A. Porporato, and L. Ridolfi, Nonlinear Dyn. NODYES 0924-090X 10.1023/A:1008335507636 23, 13 (2000).
29. B. Pilgram, K. Judd, and A. I. Mees, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(02)00534-1 170, 103 (2002).
30. K. Rodríguez-Vázquez and P. J. Fleming, Knowledge Inf. Syst. ZZZZZZ 0219-1377 8, 235 (2005).
31. J. Timmer, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127498001157 8, 1505 (1998).
32. J. Timmer, H. Rust, W. Horbelt, and H. U. Voss, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00548-X 274, 123 (2000).
33. L. M. Pecora, T. L. Carroll, and J. F. Heagy, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.3420 52, 3420 (1995).
34. K. H. Chon, J. K. Kanters, R. J. Cohen, and N. H. Holstein-Rathlou, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(96)00159-5 99, 471 (1997).
35. D. Coca and S. A. Billings, Phys. Lett. A PYLAAG 0375-9601 287, 65 (2001).
36. S. Ishii and M. A. Sato, Neural Networks NNETEB 0893-6080 14, 1239 (2001).
37. E. M. A. M. Mendes and S. A. Billings, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127497001758 7, 2593 (1997).
38. E. M. A. M. Mendes and S. A. Billings, IEEE Trans. Man Cybernet.: Part A 36, 597 (2001).
39. L. A. Aguirre and S. A. Billings, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127495000363 5, 449 (1995).
40. D. Allingham, M. West, and A. I. Mees, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 8, 2191 (1998).
41. B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056216 64, 056216 (2001).
42. G. Boudjema and B. Cazelles, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/S0960-0779(00)00163-6 12, 2051 (2001).
43. R. Brown, V. In, and E. R. Tracy, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(96)00178-9 102, 208 (1997).
44. C. S. M. Lainscsek, C. Letellier, and F. Schürrer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.016206 64, 016206 (2001).
45. J. Maquet, C. Letellier, and L. A. Aguirre, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2004.02.004 228, 421 (2004).
46. O. Ménard, C. Letellier, J. Maquet, L. Le Sceller, and G. Gouesbet, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127400001080 10, 1759 (2000).
47. C. Letellier and G. Gouesbet, J. Phys. II JPAHER 1155-4312 10.1051/jp2:1996152 6, 1615 (1996).
48. C. Letellier, L. Le Sceller, P. Dutertre, G. Gouesbet, Z. Fei, and J. L. Hudson, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100018a039 A99, 7016 (1995).
49. N. B. Tufillaro, P. Wyckoff, R. Brown, T. Schreiber, and T. Molteno, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.164 51, 164 (1995).
50. J. Theiler, S. Eubank, A. Longtin, B. Galdrijian, and J. D. Farmer, Physica D PDNPDT 0167-2789 10.1016/0167-2789(92)90102-S 58, 77 (1992).
51. J. Timmer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.5153 58, 5153 (1998).
52. M. Small and K. Judd, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97) 00311-4 117, 283 (1998).
53. C. Letellier, T. D. Tsankov, G. Byrne, and R. Gilmore, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.026212 72, 026212 (2005).
54. P. E. McSharry and L. A. Smith, Physica D PDNPDT 0167-2789 192, 1 (2004).
55. R. Brown, N. F. Rul'kov, and E. R. Tracy, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.49.3784 49, 3784 (1994).
56. R. Brown, N. F. Rulkov, and E. R. Tracy, Phys. Lett. A PYLAAG 0375-9601 194, 71 (1994).
57. C. Letellier, O. Ménard, and L. A. Aguirre, in Modeling and Forecasting Financial Data: Techniques of Nonlinear Dynamics, edited by, A. S. Soofi, and, L. Cao, (Kluwer, Dordrecht, 2002), pp. 283-302.
58. C. Sarasola, F. J. Torrrealdea, A. dAnjou, and M. Graña, Math. Comput. Simul. MCSIDR 0378-4754 10.1016/S0378-4754(01)00375-5 58, 309 (2002).
59. U. S. Freitas, E. E. N. Macau, and C. Grebogi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.047203 71, 047203 (2005).
60. A. Maybhate and R. E. Amritkar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.284 59, 284 (1999).
61. U. Parlitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1232 76, 1232 (1996).
62. L. A. B. Tôrres and L. A. Aguirre, Physica D PDNPDT 0167-2789 196, 387 (2004).
63. L. H. A. Monteiro, N. C. F. Canto, J. G. Chaui-Berlinck, F. M. Orsatti, and J. R. C. Piqueira, IEEE Trans. Neural Netw. ITNNEP 1045-9227 14, 1572 (2003).
64. L. H. A. Monteiro, M. A. Bussab, and J. G. Chaui-Berlinck, J. Theor. Biol. JTBIAP 0022-5193 219, 83 (2002).
65. R. Femat, R. Jauregui-Ortiz, and G. Solis-Perales, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. ITCAEX 1057-7122 10.1109/81.956010 48, 1161 (2001).
66. R. Gilmore and M. Lefranc, The Topology of Chaos (Wiley Interscience, New York, 2002).
67. M. Hénon, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608556 50, 69 (1976).
68. Y. Ueda, Int. J. Non-Linear Mech. IJNMAG 0020-7462 10.1016/0020-7462(85) 90024-1 20, 481 (1985).
69. P. J. Holmes, Philos. Trans. R. Soc. London, Ser. A PTRMAD 0962-8428 292, 419 (1979).
70. 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).
71. D. Yu, M. Small, R. G. Harrison, and C. Diks, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.3750 61, 3750 (2000).
72. K. Judd, Physica D PDNPDT 0167-2789 10.1016/0167-2789(92)90025-I 56, 216 (1992).
73. Y. Ueda and N. Akamatsu, IEEE Trans. Circuits Syst. ICSYBT 0098-4094 10.1109/TCS.1981.1084975 28, 217 (1981).
74. K. Judd, in Chaos and Its Reconstruction, edited by, G. Gouesbet, S. Meunier-Guttin-Cluzel, and, O. Ménard, (Nova Science, New York, 2003), pp. 179-214.
75. D. Orrell, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 15, 3265 (2005).
76. L. A. B. Tôrres (unpublished).
77. M. Small, D. Yu, and R. G. Harrison, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 13, 743 (2003).
78. G. Gouesbet, S. Meunier-Guttin-Cluzel, and O. Ménard, in Chaos and Its Reconstruction, edited by, G. Gouesbet, S. Meunier-Guttin-Cluzel, and, O. Ménard, (Nova Science, New York, 2003), pp. 1-160.
79. L. A. Aguirre and A. V. P. Souza, Comput. Biol. Med. CBMDAW 0010-4825 34, 241 (2004).
80. R. Femat and G. Solis-Perales, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036226 65, 036226 (2002).