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File:Bred vector growth rates in Lorenz system.png

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1007: 977: 524: 385: 521: 353: 203:{\displaystyle g={\frac {1}{n\Delta t}}\ln {\|\delta \mathbf {x} \|/\|\delta \mathbf {x} _{0}\|}} 86: 417: 233: 465:
Brief Communication: Breeding vectors in the phase space reconstructed from time series data
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The growth rates of bred vectors in the Lorenz system, defined as
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is the magnitude of the bred vector after the cycle, and
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230:is the number of time-steps in the breeding cycle, 432: 406: 374: 341: 314: 276: 245: 222: 202: 51:(496 × 354 pixels, file size: 14 KB, MIME type: 66: 507: 111:Bred vector growth rates in Lorenz system.png 47:Bred_vector_growth_rates_in_Lorenz_system.png 8: 309: 291: 271: 260: 196: 178: 170: 159: 562:https://creativecommons.org/licenses/by/3.0 538:– to copy, distribute and transmit the work 315:{\displaystyle \|\delta \mathbf {x} _{0}\|} 936: 589: 322:is its original magnitude. Blue indicates 1039:The following other wikis use this file: 679:Creative Commons Attribution 3.0 Unported 419: 387: 355: 328: 303: 298: 289: 266: 258: 235: 215: 190: 185: 173: 165: 158: 134: 126: 782:ea0eceb4044338f8594656604077b1d5fd5025df 1026: 909: 893: 872: 856: 835: 819: 780: 764: 746: 730: 712: 696: 676: 660: 640: 624: 607: 604: 585: 578: 277:{\displaystyle \|\delta \mathbf {x} \|} 7: 1014:User created page with UploadWizard 925: 513: 475: 598: 592: 529: 504: 460: 237: 143: 115: 98: 44: 597: 568:Creative Commons Attribution 3.0 469:Nonlinear Processes in Geophysics 407:{\displaystyle 3.2\leq g\leq 6.4} 583: 549:Under the following conditions: 520:This file is licensed under the 512: 506: 299: 267: 253:is the length of the time-step, 186: 166: 65: 31: 21: 580: 375:{\displaystyle 0\leq g\leq 3.2} 116: 41:No higher resolution available. 14: 579: 26: 1: 605:Items portrayed in this file 1075: 1053:Usage on www.wikidata.org 1043:Usage on pt.wikipedia.org 926: 433:{\displaystyle 6.4\leq g} 16: 582: 525:Attribution 3.0 Unported 246:{\displaystyle \Delta t} 72:This is a file from the 1013: 992:20:39, 26 November 2017 983: 962:20:57, 26 November 2017 489: 482:10.5194/npg-23-137-2016 454: 447: 444: 108: 76:. Information from its 434: 408: 376: 343: 342:{\displaystyle g<0} 316: 278: 247: 224: 204: 79:description page there 435: 409: 377: 344: 317: 279: 248: 225: 205: 794:determination method 418: 414:, and red indicates 386: 354: 327: 288: 257: 234: 214: 125: 544:– to adapt the work 430: 404: 372: 350:, green indicates 339: 312: 274: 243: 220: 200: 1035:Global file usage 1017: 663:copyright license 591: 497: 496: 223:{\displaystyle n} 150: 94: 93: 74:Wikimedia Commons 32:Global file usage 1066: 1047:Vetor de criação 1009:InverseHypercube 1004: 979:InverseHypercube 974: 914: 877: 840: 803: 798: 627:copyright status 575: 572: 569: 566: 563: 522:Creative Commons 516: 515: 510: 509: 485: 479: 462: 450: 439: 437: 436: 431: 413: 411: 410: 405: 381: 379: 378: 373: 349: 346: 345: 340: 321: 319: 318: 313: 308: 307: 302: 283: 281: 280: 275: 270: 252: 250: 249: 244: 229: 227: 226: 221: 209: 207: 206: 201: 199: 195: 194: 189: 177: 169: 151: 149: 135: 120: 112: 106: 90: 69: 68: 62: 56: 54: 1074: 1073: 1069: 1068: 1067: 1065: 1064: 1063: 1033: 1025: 1018: 1010: 1002: 980: 972: 928: 927: 924: 923: 922: 921: 920: 919: 918: 917: 915: 912: 902: 901: 900: 898: 887: 886: 885: 884: 883: 882: 881: 880: 878: 875: 865: 864: 863: 861: 850: 849: 848: 847: 846: 845: 844: 843: 841: 838: 828: 827: 826: 824: 813: 812: 811: 810: 809: 808: 807: 806: 805: 804: 801:saquina chaúque 799: 796: 787: 786: 785: 783: 773: 772: 771: 769: 758: 757: 756: 755: 754: 753: 752: 751: 749: 739: 738: 737: 735: 724: 723: 722: 721: 720: 719: 718: 717: 715: 705: 704: 703: 701: 690: 689: 688: 687: 686: 685: 684: 683: 681: 669: 668: 667: 665: 654: 653: 652: 651: 650: 649: 648: 647: 645: 633: 632: 631: 629: 618: 617: 616: 615: 614: 612: 596: 595: 594: 577: 576: 573: 570: 567: 564: 561: 560: 528: 517: 503: 498: 458: 440: 416: 415: 384: 383: 352: 351: 324: 323: 297: 286: 285: 255: 254: 232: 231: 212: 211: 184: 139: 123: 122: 110: 103: 96: 95: 84: 83: 82:is shown below. 58: 52: 50: 43: 42: 12: 11: 5: 1072: 1070: 1062: 1061: 1060: 1059: 1051: 1050: 1049: 1037: 1036: 1032: 1031: 1023: 1022: 1021: 1016: 1015: 1012: 1008: 1005: 999: 994: 989: 986: 985: 982: 978: 975: 969: 964: 959: 955: 954: 951: 948: 945: 942: 939: 932: 931: 916: 910: 908: 907: 906: 905: 904: 903: 899: 894: 892: 891: 890: 889: 888: 879: 873: 871: 870: 869: 868: 867: 866: 862: 857: 855: 854: 853: 852: 851: 842: 836: 834: 833: 832: 831: 830: 829: 825: 820: 818: 817: 816: 815: 814: 792: 791: 790: 789: 788: 784: 781: 779: 778: 777: 776: 775: 774: 770: 765: 763: 762: 761: 760: 759: 750: 747: 745: 744: 743: 742: 741: 740: 736: 731: 729: 728: 727: 726: 725: 716: 713: 711: 710: 709: 708: 707: 706: 702: 697: 695: 694: 693: 692: 691: 682: 677: 675: 674: 673: 672: 671: 670: 666: 661: 659: 658: 657: 656: 655: 646: 641: 639: 638: 637: 636: 635: 634: 630: 625: 623: 622: 621: 620: 619: 613: 608: 606: 603: 602: 601: 600: 599: 588: 587: 584: 581: 559: 558: 557: 556: 547: 546: 545: 539: 532:You are free: 519: 518: 505: 502: 499: 495: 494: 491: 487: 486: 456: 452: 451: 446: 442: 441: 429: 426: 423: 403: 400: 397: 394: 391: 371: 368: 365: 362: 359: 348: 338: 335: 332: 326: 311: 306: 301: 296: 293: 273: 269: 265: 262: 242: 239: 219: 198: 193: 188: 183: 180: 176: 172: 168: 164: 161: 157: 154: 148: 145: 142: 138: 133: 130: 113: 104: 102: 99: 97: 92: 91: 70: 60: 59: 40: 36: 35: 34: 29: 24: 19: 13: 10: 9: 6: 4: 3: 2: 1071: 1058: 1055: 1054: 1052: 1048: 1045: 1044: 1042: 1041: 1040: 1034: 1030: 1027: 1019: 1011: 1006: 1000: 998: 995: 993: 990: 988: 987: 981: 976: 970: 968: 965: 963: 960: 957: 956: 952: 949: 946: 943: 940: 938: 937: 935: 929: 897: 860: 823: 802: 795: 768: 734: 700: 680: 664: 644: 628: 611: 554: 551: 550: 548: 543: 540: 537: 534: 533: 531: 530: 526: 523: 511: 500: 492: 488: 483: 478: 473: 470: 466: 457: 453: 443: 427: 424: 421: 401: 398: 395: 392: 389: 369: 366: 363: 360: 357: 336: 333: 330: 304: 294: 263: 240: 217: 191: 181: 174: 162: 155: 152: 146: 140: 136: 131: 128: 119: 114: 107: 100: 88: 81: 80: 75: 71: 64: 63: 57: 48: 39: 33: 30: 28: 25: 23: 20: 18: 15: 1038: 933: 930:File history 714:10 June 2016 552: 541: 535: 471: 468: 461:10 June 2016 449:10 June 2016 117: 87:You can help 77: 45: 22:File history 1029:Bred vector 643:copyrighted 553:attribution 474:: 137-141. 109:Description 1020:File usage 1001:560 × 420 971:496 × 354 947:Dimensions 733:media type 565:CC BY 3.0 27:File usage 944:Thumbnail 941:Date/Time 822:data size 748:image/png 699:inception 501:Licensing 118:English: 53:image/png 1057:Q4960091 767:checksum 586:Captions 542:to remix 536:to share 527:license. 210:, where 984:Cropped 973:(14 KB) 958:current 953:Comment 837:14,500 610:depicts 590:English 101:Summary 49:‎ 1003:(7 KB) 859:height 490:Author 455:Source 913:pixel 896:width 876:pixel 950:User 911:496 874:354 839:byte 574:true 571:true 463:). " 445:Date 334:< 17:File 477:DOI 467:". 422:6.4 402:6.4 390:3.2 370:3.2 797:: 472:23 425:≤ 399:≤ 393:≤ 382:, 367:≤ 361:≤ 310:‖ 295:δ 292:‖ 272:‖ 264:δ 261:‖ 238:Δ 197:‖ 182:δ 179:‖ 171:‖ 163:δ 160:‖ 156:⁡ 153:ln 144:Δ 484:. 480:: 428:g 396:g 364:g 358:0 337:0 331:g 305:0 300:x 268:x 241:t 218:n 192:0 187:x 175:/ 167:x 147:t 141:n 137:1 132:= 129:g 89:. 55:)

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File:Bred vector growth rates in Lorenz system.png
Bred_vector_growth_rates_in_Lorenz_system.png
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Brief Communication: Breeding vectors in the phase space reconstructed from time series data
DOI
10.5194/npg-23-137-2016
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20:57, 26 November 2017
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