Polynomial search and global modeling: Two algorithms for modeling chaos

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

Volumn 86, Issue 4, 2012, Pages

  Mangiarotti, S ^a   Coudret, R ^a   Drapeau, L ^a   Jarlan, L ^a  

^a CNES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRODISSOLUTION; EXPERIMENTAL ANALYSIS; FIRST RETURNS; GLOBAL MODELING; GLOBAL MODELS; LYAPUNOV EXPONENT; POINCARE; POLYNOMIAL MODELS; POLYNOMIAL SEARCHES; RAINFED; SEMIARID CLIMATIC CONDITION; SINGLE TIME SERIES; SPATIAL SENSORS; VEGETATION INDEX;

ALGORITHMS; DYNAMICAL SYSTEMS; LYAPUNOV METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PHOSPHORIC ACID; POLYNOMIALS; TIME SERIES;

MATHEMATICAL MODELS;

EID: 84867454237     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.046205     Document Type: Article

References (51)

1. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Physica D 0167-2789 10.1016/0167-2789(85)90011-9 16, 285 (1985).
2. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.50.346 50, 346 (1983).
3. N. B. Tufillaro, T. Abbott, and J. Reilly, An Experimental Approach to Nonlinear Dynamics and Chaos (Addison-Wesley, New York, 1992).
4. R. Gilmore, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.1455 70, 1455 (1998). (Pubitemid 128159252)
5. R. Gilmore and M. Lefranc, The Topology of Chaos, Alice in Stretch and Squeezeland (Wiley, New York, 2002), p. 495.
6. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, Physica D 0167-2789 10.1016/0167-2789(92)90102-S 58, 77 (1992).
7. M. E. D. Gomes, A. V. P. Souza, H. N. Guimarães, and L. A. Aguirre, Chaos CHAOEH 1054-1500 10.1063/1.166507 10, 398 (2000).
8. C.-S. Poon and M. Barahona, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.131173198 98, 7107 (2001). (Pubitemid 32567910)
9. U. Freitas, C. Letellier, and L. Aguirre, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.035201 79, 035201 (2009).
10. D. T. Kaplan and L. Glass, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.427 68, 427 (1992).
11. G. Gouesbet and C. Letellier, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.49.4955 49, 4955 (1994).
12. C. Letellier, L. A. Aguirre, and U. S. Freitas, Chaos 1054-1500 10.1063/1.3125705 19, 023103 (2009).
13. K. Judd and I. Mees, Physica D 0167-2789 10.1016/0167-2789(95)00050-E 82, 426 (1995).
14. C. Letellier, L. Le Sceller, E. Maréchal, P. Dutertre, B. Maheu, G. Gouesbet, Z. Fei, and J. L. Hudson, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.51.4262 51, 4262 (1995).
15. 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).
16. C. Letellier, J. Maquet, H. Labro, L. Le Sceller, G. Gouesbet, F. Argoul, and A. Arnéodo, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp982219u 102, 10265 (1998).
17. C. Letellier, O. Ménard, Th. Klinger, A. Piel, and G. Bonhomme, Physica D 0167-2789 10.1016/S0167-2789(01)00279-2 156, 169 (2001). (Pubitemid 32594702)
18. M. V. Corrêa, E. M. A. M. Mendes, and L. A. Aguirre, Int. J. Bifurcation Chaos 10.1142/S0218127400000724 10, 1019 (2000).
19. C. Letellier, L. A. Aguirre, J. Maquet, and R. Gilmore, Astron. Astrophys. AAEJAF 0004-6361 10.1051/0004-6361:20053947 449, 379 (2006).
20. J. Maquet, C. Letellier, and L. A. Aguirre, J. Math. Biol. 0303-6812 10.1007/s00285-007-0075-9 55, 21 (2007). (Pubitemid 47145808)
21. R. Hegger, H. Kantz, and T. Schreiber, Chaos CHAOEH 1054-1500 10.1063/1.166424 9, 413 (1999).
22. PoMoS & GloMo can be freely downloaded at the following address: http://www.cesbio.ups-tlse.fr/us/pomos-et-glomo.html
23. R. Ihaka and R. Gentleman, J. Comput. Graphical Stat. 5, 299 (1996);
24. see also the Comprehensive R Archive Network's Web site at http://cran.r-project.org/.
25. J. M. Chambers, Software for Data Analysis: Programming with R (Springer, New York, 2008);
26. see also the Comprehensive R Archive Network's website at http://cran.r-project.org/
27. F. Takens, in Lecture Notes in Mathematics, edited, D. Rand, and, L. S. Young, Vol. 898 (Springer Verlag, Berlin, 1981), pp. 366-381.
28. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.45.712 45, 712 (1980).
29. M. B. Kennel and H. D. I. Abarbanel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.026209 66, 026209 (2002). (Pubitemid 40618731)
30. C. Letellier, I. M. Moroz, and R. Gilmore, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.026203 78, 026203 (2008).
31. C. Lainscsek, C. Letellier, and F. Schürrer, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.016206 64, 016206 (2001).
32. L. A. Aguirre and S. A. Billings, Physica D 0167-2789 10.1016/0167-2789(95)90053-5 80, 26 (1995).
33. S. A. Billings, S. Chen, and M. J. Korenberg, Int. J. Control 49, 2157 (1989).
34. L. A. Aguirre and C. R. F. Jácome, IEE Proc.-D: Control Theory Appl. 1350-2379 10.1049/ip-cta:19982112 145, 409 (1998).
35. L. A. Aguirre, U. S. Freitas, C. Letellier, and J. Maquet, Physica D 0167-2789 10.1016/S0167-2789(01)00313-X 158, 1 (2001). (Pubitemid 32903826)
36. C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.066213 71, 066213 (2005). (Pubitemid 41663857)
37. 3); (2) for the electrodissolution of copper in phosphoric acid; and (3) for the cycles of rainfed wheat observed from satellite data in northern Morocco.
38. O. Rössler, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(76) 90101-8 57, 397 (1976).
39. M. R. Bassett and J. L. Hudson, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100344a009 93, 2731 (1989).
40. Z. Fei, J. L. Hudson, and R. G. Kelly, J. Electrochem. Soc. JESOAN 0013-4651 10.1149/1.2055175 141, L123 (1994).
41. C. J. Tucker, J. E. Pinzon, M. E. Brown, D. A. Slayback, E. W. Pak, R. Mahoney, E. F. Vermote, and N. E. Saleous, Int. J. Remote Sens. 0143-1161 10.1080/01431160500168686 26, 4485 (2005).
42. C. J. Tucker, Remote Sens. Environ. RSEEA7 0034-4257 10.1016/0034- 4257(79)90013-0 8, 127 (1979). (Pubitemid 9444868)
43. L. Jarlan, Y. Tourre, E. Mougin, N. Philippon, and P. Mazzega, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2004GL021841 32, L04701 (2005). (Pubitemid 40746871)
44. S. Mangiarotti, P. Mazzega, L. Jarlan, E. Mougin, F. Baup, and J. Demarty, Remote Sens. Environ. 0034-4257 10.1016/j.rse.2007.03.030 112, 1365 (2008). (Pubitemid 351384728)
45. P. Mayaux, E. Bartholomé, S. Fritz, and A. Belward, J. Biogeogr. 0305-0270 10.1111/j.1365-2699.2004.01073.x 31, 861 (2004). (Pubitemid 38681828)
46. A. Savitzky and M. J. E. Golay, Anal. Chem. ANCHAM 0003-2700 10.1021/ac60214a047 36, 1627 (1964).
47. C. Lainscsek, C. Letellier, and I. Gorodnitsky, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00912-5 314, 409 (2003).
48. C. Letellier, J. Maquet, L. Le Sceller, G. Gouesbet, and L. Aguirre, J. Phys. A JPHAC5 1361-6447 10.1088/0305-4470/31/39/008 31, 7913 (1998). (Pubitemid 128139558)
49. L. Le Sceller, C. Letellier, and G. Gouesbet, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.1600 60, 1600 (1999).
50. H. Akaike, IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/TAC.1974.1100705 19, 716 (1974).
51. G. Schwarz, Ann. Stat. ASTSC7 0090-5364 10.1214/aos/1176344136 6, 461 (1978).