Simulação - Atividades (Aula 3)
Ana Cláudia Lima
05/09/2018
Finalidade
Esta atividade tem o objetivo de Construir sequencia descrita em classe (x[n+1] = x²[n] + e[n], x[0] = e[0]) e plotar diagrama de Poincaré (x[n+1] vs x[n]).
set.seed(123)
x0 = rnorm(1,0,1)
vetor = rep(1:999-1:999) #Cria um vetor vazio com 999 observações
x = c(x0,vetor)
for (i in 1:999) {
x[i+1] = (((x[i]^2) %% 100) + rnorm(1,0,1))
}
x## [1] -0.56047565 0.08395546 1.56575683 2.52210285 6.49029054
## [6] 43.83893625 22.31324774 96.61596363 33.95757503 52.67123995
## [11] 75.48359925 98.13357008 30.59834785 36.36957370 22.19005023
## [16] 94.18524250 71.35775491 89.96256880 93.96514010 28.97476229
## [21] 38.46902607 79.64799160 42.77656067 29.10525147 46.49062410
## [26] 59.69143558 63.90526835 84.03669584 61.02811102 25.68414969
## [31] 60.10200942 11.95646530 43.85218823 23.89254573 71.67532251
## [36] 38.04049670 47.63330677 68.87000222 42.77124360 28.99880851
## [41] 40.23618780 18.74289149 50.03058501 5.22839287 28.54405398
## [46] 13.63990910 85.64423540 34.46840262 88.85074401 94.37134170
## [51] 6.20345313 38.45428395 78.68908350 93.34046495 12.21662521
## [56] 50.76240210 75.27271424 66.56612350 31.17265211 71.95018138
## [61] 77.20824079 60.61012253 73.25374514 65.09260165 35.97499826
## [66] 94.50402824 31.45956289 89.75710120 57.25948283 80.69845851
## [71] 11.75017471 35.75743688 79.60003103 35.45573845 56.42138062
## [76] 84.39776204 22.69746452 13.95417788 94.90038369 5.94393373
## [81] 35.33611241 49.02612064 3.18984464 10.81948540 16.84077781
## [86] 83.94357922 47.62133171 68.22641561 54.51785540 73.34536452
## [91] 80.53600075 86.59581360 99.07366555 14.96329854 25.26095577
## [96] 37.51562689 9.60959404 93.87690817 12.63818802 58.69737560
## [101] 44.67149615 95.79945203 77.28831816 73.13658122 48.00789341
## [106] 4.71280206 21.42559880 57.38834217 93.04159106 57.65666354
## [111] 23.71550337 63.03306444 71.54932936 19.25097057 71.11927510
## [116] 58.25244452 93.45296914 32.81673459 76.08836477 88.41512454
## [121] 17.35189479 0.14077828 -0.47073892 -0.03449706 1.84505205
## [126] 2.75226717 7.81036117 61.07970253 29.76820419 86.07467252
## [131] 10.29379993 6.41382111 41.17833411 95.23270309 67.21449116
## [136] 18.91915851 56.47391872 90.04344263 9.73066379 93.24192466
## [141] 94.75829944 78.87311534 19.39617941 74.69710815 78.05642937
## [146] 92.27525946 13.26175214 76.56198648 63.83788291 73.98826429
## [151] 75.05099184 33.42041854 17.25657765 96.78109543 66.46097996
## [156] 16.78146193 82.18045394 53.25457076 37.02628055 70.57087043
## [161] 81.30046465 8.71637510 74.71503956 85.57817634 23.20740761
## [166] 38.88199579 12.44616634 54.42327604 62.40983655 95.35666323
## [171] 92.67784216 89.24772051 65.12154934 42.94464073 43.50083114
## [176] 91.22631381 22.27812020 96.62512053 36.85044064 57.49661023
## [181] 4.79686221 24.27307220 88.83238365 90.32687208 58.70753974
## [186] 46.37804671 52.03313717 7.53210075 57.48659548 4.20936821
## [191] 17.93322607 21.27591132 52.75898581 82.61522065 23.96388120
## [196] 76.26481577 16.92283294 85.13100325 46.67654797 77.51465008
## [201] 10.71978767 16.22626061 63.02638832 72.86881850 9.45036987
## [206] 88.83324379 90.55659967 -0.09687349 1.66029194 2.70254120
## [211] 7.42297418 55.34423317 64.21662140 23.25839957 39.96064356
## [216] 98.52873053 7.46957722 55.07151790 31.63581072 -0.46019600
## [221] -0.36219312 0.74916967 1.67110334 3.50017471 11.88756571
## [226] 41.37396855 11.10067735 22.50781943 7.48658602 55.03337771
## [231] 30.62795650 37.98139982 42.80127100 31.21027190 73.50668334
## [236] 1.91547892 3.48613410 12.57211336 58.38233865 7.71593033
## [241] 58.74695891 50.70298249 72.28849433 24.48910959 99.53743684
## [246] 9.60369435 92.12997028 86.57158342 93.97428668 31.65201763
## [251] 1.47461710 1.61261922 2.25662352 5.18284636 28.46040517
## [256] 9.90609729 99.21156293 43.56497282 97.79321705 61.98039992
## [261] 41.04885714 84.51880216 43.47507293 91.38216467 52.99309849
## [266] 9.81606867 96.22205310 56.92697548 40.29175744 23.51492479
## [271] 53.79670095 95.04756127 34.72321204 4.30617972 19.39282684
## [276] 75.63517556 20.85458510 34.98827102 24.60727595 5.54270460
## [281] 29.05409922 44.87717754 14.34709062 5.57335751 31.18045841
## [286] 72.35502547 35.47073092 59.81359800 77.44745488 98.27633220
## [291] 59.40585395 30.10966402 7.73713065 59.28572269 16.79939781
## [296] 82.28646775 72.92962721 17.37962167 2.07223299 5.54406413
## [301] 30.02140487 0.53206133 -0.65544944 -0.62289930 -0.04915599
## [306] 0.33359548 -1.90292455 3.83310228 15.92934813 55.78170590
## [311] 12.89988920 67.16391607 9.26489144 85.23670667 64.94411832
## [316] 18.44202830 40.00273647 -1.03972320 2.76546005 8.55916059
## [321] 73.49666020 2.97716989 7.52476628 57.28292785 80.81091042
## [326] 31.08698845 66.34002924 1.63244019 4.00037859 16.01031894
## [331] 57.34787105 87.58987990 71.26545657 80.28451811 45.98123541
## [336] 12.22178689 48.00803725 4.57085998 21.75854037 73.33219558
## [341] 78.23509562 21.68919146 72.09208119 97.32418689 71.94537165
## [346] 74.38326461 32.96938225 86.40831589 65.42304527 79.99494557
## [351] 100.20625992 39.30177872 44.20253090 53.98037569 12.98775157
## [356] 69.01559376 63.56361135 40.29965115 21.59598484 68.95801918
## [361] 55.00310958 25.99325649 75.92314946 65.34929652 71.34821473
## [366] 90.35795142 64.93755334 15.94042487 54.95406802 19.48855334
## [371] 82.22048478 58.55706907 28.46635131 11.15853704 25.02308139
## [376] 25.56512107 52.57863461 64.65729268 80.55118898 86.70376446
## [381] 17.57732345 9.15253001 83.94353202 45.46155049 67.22870668
## [386] 21.07757196 44.72027596 98.76749310 54.58204829 79.54609947
## [391] 26.93489528 23.33093731 45.21688659 43.73735506 12.38266702
## [396] 54.83434308 6.03103568 37.21912288 84.00242477 56.05282542
## [401] 41.84568136 49.89239728 88.61655831 52.86556556 95.43871834
## [406] 6.89841215 47.23833595 32.21678998 37.38274743 97.69709763
## [411] 45.21511343 44.67431740 96.44789318 2.07339057 3.88527196
## [416] 12.45218925 54.96407610 21.47994585 61.92347255 33.96117468
## [421] 55.14088829 40.80398565 65.09156084 38.18355953 57.26575190
## [426] 78.91600151 30.13274672 7.99355392 65.53047267 92.80434166
## [431] 12.45531352 55.51325871 82.02193158 26.59162393 7.13372260
## [436] 49.81257743 82.00557353 25.99886502 73.71599446 35.28353239
## [441] 43.68661353 8.97497060 81.20999993 94.86419922 98.57117944
## [446] 16.44273633 70.80239680 13.86269506 90.12197727 20.33440704
## [451] 14.91851186 23.60862492 57.80245954 41.83950727 51.46154372
## [456] 45.62955931 83.16695989 16.25822906 64.56062892 67.77964863
## [461] 94.95273365 15.67315564 46.16631158 30.93763970 56.04476304
## [466] 42.22547479 83.73162136 12.70867815 61.57565416 92.68618843
## [471] 92.70494538 93.92541540 20.66070626 26.62543162 8.69956795
## [476] 75.83416295 52.53257537 59.34533112 22.24133015 94.44908262
## [481] 20.64965898 26.72247385 15.41882341 37.86143386 34.20101600
## [486] 70.48835535 69.52301273 32.87490443 82.38622241 87.10868703
## [491] 87.81757112 13.32984755 78.97891949 36.57973131 37.20367175
## [496] 82.75511286 48.59055186 61.20657055 46.60839350 72.89450236
## [501] 13.00658080 68.17744557 49.19086905 20.49265921 18.43991512
## [506] 39.93532216 93.93400836 21.52717540 63.56940076 40.98950157
## [511] 80.04186946 6.91701849 48.72761001 74.58557499 62.39156118
## [516] 91.97210697 58.73665732 50.30493053 29.54635505 72.80278787
## [521] 1.21318860 1.36354648 1.16083833 1.07160046 2.26297608
## [526] 5.67110471 33.39810443 15.57247718 42.91232070 40.90881056
## [531] 74.13615197 95.66269487 49.93062505 93.19531081 87.31180911
## [536] 24.15292467 84.52902368 45.51469938 70.97930292 37.85920178
## [541] 33.04591128 91.56355246 84.58830618 53.98417836 15.15787959
## [546] 30.62546609 36.72055108 49.03836358 7.19132930 51.15800158
## [551] 17.98603001 22.71507364 17.08528207 92.15668810 94.50707608
## [556] 30.12845922 7.67275691 58.34427349 3.85698477 14.24675280
## [561] 2.13612170 5.14173830 25.34989208 44.10105936 43.71722981
## [566] 11.29726117 28.16109916 93.63424149 67.06943326 98.38837975
## [571] 81.23453465 97.59315327 23.64182528 59.25630493 10.86489252
## [576] 19.41589349 77.65017394 29.62167939 75.93613277 66.32236005
## [581] 98.33902662 70.46181056 63.68518829 56.30186546 68.86109749
## [586] 41.62452588 32.98258035 87.06709056 81.26124927 2.07412330
## [591] 1.49221280 2.69166702 8.08561119 65.09126294 37.37663794
## [596] 95.85714738 88.46555563 24.21301401 87.45122844 49.57726679
## [601] 58.97939485 78.54166980 68.76056480 26.49920427 2.99821250
## [606] 8.77854400 76.40609191 36.47885440 30.40705613 23.74000114
## [611] 63.19062355 91.83730457 35.77809932 80.05638828 10.10024910
## [616] -0.58666777 -0.10901875 -0.66359720 -0.78256493 2.15901703
## [621] 3.24607260 10.85537758 18.68565865 49.33202921 32.77385034
## [626] 75.06643188 35.13978275 33.74083411 37.05583754 75.22181331
## [631] 57.64269403 20.82460352 34.19737121 69.77042803 66.55879374
## [636] 28.13006756 91.18439852 15.73392942 48.19265907 22.03945066
## [641] 84.90319737 8.82399118 78.02017365 87.77720751 4.44236038
## [646] 20.63391976 24.92783314 21.06632053 44.53067511 83.97099770
## [651] 49.18995020 19.75839098 91.00279324 80.05755330 9.69246541
## [656] 93.11571141 71.55596488 20.79459257 33.18413238 1.30736136
## [661] 2.57284217 8.00003136 65.96674970 51.58367084 58.62604623
## [666] 37.04482304 72.52447495 59.64412194 57.98957107 63.80103036
## [671] 70.05349291 7.19777409 52.20579407 24.89471049 19.83787775
## [676] 91.57968621 85.71902685 46.42380945 54.31646055 49.58458269
## [681] 59.01314553 83.53345781 77.11119064 45.13888340 36.47710607
## [686] 30.16467840 9.66879381 93.96919130 29.88758912 91.18949435
## [691] 15.43244485 39.34754073 49.42056242 41.60302652 29.26403879
## [696] 58.84202677 62.22169192 71.44149471 4.30774069 16.94259039
## [701] 86.32314990 50.14576576 13.90472891 93.46033556 33.46961414
## [706] 20.80505328 33.13958614 97.32795430 72.95701379 23.47394216
## [711] 52.08705576 12.84852931 64.99106863 23.75228721 65.61260947
## [716] 6.13959367 38.52901199 84.19742414 89.57947380 24.88541593
## [721] 18.24225296 31.05148844 64.83676441 2.27670819 5.18508388
## [726] 27.13534269 36.89069010 61.11244254 33.99777914 56.83535224
## [731] 31.99589799 24.61866668 4.13509810 18.49861250 42.14260855
## [736] 76.52437009 56.60125020 3.60483855 12.91959779 67.93516406
## [741] 15.89811789 53.74041473 90.41510163 75.55501813 8.76814627
## [746] 74.66975596 78.26416950 24.79755104 17.29327240 99.43191399
## [751] 88.24394954 86.88491933 49.50067829 50.53110904 53.20686040
## [756] 30.84959976 52.71063959 78.21006795 14.77704569 18.16519000
## [761] 30.51391843 31.71567382 6.50053370 40.56483681 45.87472752
## [766] 5.45848386 31.07162476 65.22090376 53.44439504 57.79119923
## [771] 38.15478005 55.35041093 64.12545264 10.45590205 9.60551561
## [776] 94.14379422 63.04993028 75.01525437 27.76330009 70.52175963
## [781] 74.13198139 96.45509969 3.58894775 11.70385381 35.66197320
## [786] 71.18333547 67.86462843 3.64958661 11.43315726 30.06330520
## [791] 4.19671465 16.69884784 79.73826832 58.52480386 24.98202751
## [796] 24.92052655 21.42100886 58.41368544 12.38976179 54.15371052
## [801] 32.98064630 87.06502023 81.17294920 90.20061756 36.42768241
## [806] 27.12015057 35.42694167 57.22961204 75.50480946 0.81795752
## [811] -1.83886330 1.81613646 3.22067842 10.57906355 12.19345805
## [816] 49.50192598 50.24652302 25.92766486 71.32228884 85.66044213
## [821] 36.48235965 31.70486293 5.11541328 26.95727092 26.42674900
## [826] 97.78117051 60.78895338 93.44423570 30.65557101 38.32199926
## [831] 69.62994985 47.73258666 79.18928949 72.46006128 50.26870652
## [836] 27.22673389 39.54397072 62.90695081 57.34067504 88.25210103
## [841] 87.67393800 89.40426267 92.66379331 86.64283344 7.63037798
## [846] 58.19664945 86.20644006 32.59561280 64.08951933 7.43679449
## [851] 55.86817969 21.15608919 48.59656491 60.46995331 58.93611378
## [856] 72.86197656 7.40877868 54.53908368 74.65835696 75.49388563
## [861] 100.23797667 47.79442582 82.91765635 74.47169697 45.87036505
## [866] 6.64341627 42.27475216 88.28572505 93.84201299 7.98939226
## [871] 62.69118805 30.32868199 18.72940043 51.69395700 73.74896957
## [876] 40.86123357 70.43800960 63.35646251 15.28776580 33.58390822
## [881] 28.35592830 3.08667536 9.34236264 88.50070338 32.91578369
## [886] 83.90617351 39.20782153 36.64875606 42.36671505 95.33384004
## [891] 87.55054903 65.66067744 10.20814568 6.03476873 36.87902499
## [896] 59.36148089 24.02645931 76.91829379 16.79506730 82.31781846
## [901] 75.20912180 55.62068797 93.96052446 30.21920843 14.28517513
## [906] 3.44166096 12.67095310 60.50448409 61.09390907 32.72608723
## [911] 73.57223546 11.68854133 36.72291821 46.79274454 90.15077755
## [916] 28.25930072 100.03373921 4.82383516 23.68215514 62.43784183
## [921] 98.07007623 17.52770040 7.18374397 51.97119624 1.67039849
## [926] 4.10805199 16.78060359 81.78493477 91.26355326 29.46725326
## [931] 68.50776789 91.97201777 58.85490926 63.67901831 55.00632708
## [936] 25.12060114 30.35778606 20.87440077 35.52610300 63.47212697
## [941] 29.75998832 85.29692967 73.88029438 57.45331381 0.42550776
## [946] 0.28469486 -0.58155611 2.34488820 5.22623316 26.09956853
## [951] 81.04621574 67.48370772 54.20696302 38.62847391 92.51458458
## [956] 57.32650208 86.54855153 90.96222182 72.70469008 86.92732570
## [961] 57.14412367 67.75048943 90.28552107 51.52204795 54.61801119
## [966] 83.19691258 19.87779080 93.45544000 33.84172613 44.68136014
## [971] 96.47868043 6.02456905 34.79673396 9.71121055 95.29366855
## [976] 79.78477638 64.81102748 0.54915693 -0.02117303 0.14686548
## [981] 2.32663145 4.28861023 18.08670809 26.61225012 9.72425173
## [986] 93.79158671 96.77965032 67.08784956 -0.27903179 1.73303455
## [991] 3.67917118 12.46209395 55.75836338 8.78177926 77.43287567
## [996] 95.76025858 71.09764009 53.52332659 64.22387305 24.45667848Gráfico
plot(x[-1000],x[-1])
Diagrama de Poincaré
plot(x[-1000],x[-1], type = "l")