QM 2512 Tabla Lotka pdf

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(1)Sheet1. Lotka-Volterra Model of a Predator-Prey System Time t. Prey H(t). Predator P(t). 0. 50. 15. 1. dH/dt = rH - aPH dP/dt = bPH - mP. Parameters. r a b m. 47,5625 14,98125. 2 45,26077 14,92705 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45. 43,1013 41,08726 39,21908 37,495 35,91159 34,46422 33,14739 31,95515 30,88127 29,91952 29,06375 28,3081 27,64699 27,07526 26,58813 26,18126 25,85078 25,59321 25,4055 25,28505 25,2296 25,23729 25,30661 25,43638 25,62574 25,87412 26,18123 26,54703 26,97172 27,45572 27,99967 28,60438 29,27081 30,0001 30,7935 31,65233 32,57802 33,57203 34,63583 35,77085 36,97846 38,25991 39,61627. 14,83987 14,72243 14,57757 14,40825 14,21736 14,00779 13,78225 13,54338 13,2936 13,03517 12,77019 12,50054 12,22795 11,95395 11,67992 11,40709 11,13655 10,86924 10,606 10,34755 10,09453 9,847459 9,606816 9,372992 9,146323 8,927094 8,715542 8,511869 8,316243 8,128806 7,949678 7,778963 7,616752 7,463129 7,318171 7,181957 7,054568 6,936089 6,826617 6,72626 6,635142 6,553406 6,481216. 0,1 0,01 0,001 0,05. 100 80 60 40 20 0 1. 19. 37. 55. 73. 91 109 127 145 163 181. 16 14 12 10 8 6 4 2 0 0. 20. 40. Page 1. 60. 80. 100.

(2) Sheet1. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97. 41,04837 42,55674 44,1415 45,80232 47,53826 49,3477 51,22821 53,17641 55,18783 57,25676 59,37608 61,53711 63,72945 65,94083 68,15695 70,3614 72,53556 74,65863 76,70762 78,65755 80,48168 82,1519 83,63926 84,91463 85,94958 86,71727 87,1936 87,35835 87,19627 86,69818 85,86181 84,69244 83,20314 81,4146 79,35454 77,05671 74,55957 71,90466 69,13491 66,293 63,41977 60,553 57,7264 54,96902 52,3049 49,75313 47,32803 45,03957 42,8939 40,89387 39,03967 37,32935. 6,41876 6,366256 6,32395 6,292126 6,271101 6,261233 6,262924 6,27662 6,302812 6,342042 6,394897 6,462014 6,544072 6,641791 6,755923 6,88724 7,036521 7,204528 7,391983 7,599534 7,827716 8,076901 8,347246 8,638631 8,950591 9,282254 9,632272 9,998766 10,37929 10,77079 11,16964 11,57168 11,97226 12,36639 12,74888 13,1145 13,45818 13,77521 14,06135 14,31306 14,52753 14,7028 14,83773 14,93202 14,98611 15,00113 14,97876 14,92117 14,83084 14,71052 14,56307 14,39143. Page 2.

(3) Sheet1. 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149. 35,75934 34,32489 33,02046 31,84004 30,77739 29,82627 28,98057 28,23442 27,58231 27,01909 26,54004 26,14086 25,8177 25,56713 25,38616 25,2722 25,22305 25,23687 25,3122 25,44787 25,64307 25,89724 26,21013 26,58172 27,01223 27,50211 28,05201 28,66275 29,33534 30,0709 30,87069 31,73607 32,66846 33,66932 34,74011 35,88228 37,09718 38,38604 39,74993 41,18964 42,70567 44,29811 45,96656 47,71003 49,52684 51,41445 53,36941 55,38711 57,46173 59,58599 61,75107 63,94638. 14,19851 13,98717 13,76014 13,52002 13,26921 13,00999 12,74439 12,47431 12,20145 11,92732 11,6533 11,3806 11,11027 10,84328 10,58043 10,32244 10,06993 9,823428 9,583397 9,350223 9,124237 8,905717 8,694899 8,491978 8,297121 8,110467 7,932135 7,762227 7,600832 7,448033 7,303909 7,168537 7,041999 6,924381 6,81578 6,716307 6,626086 6,545262 6,474002 6,412497 6,360966 6,319661 6,288867 6,268905 6,260139 6,262974 6,27786 6,305294 6,345822 6,400037 6,468579 6,552133. Page 3.

(4) Sheet1. 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197. 66,15945 68,3758 70,57878 72,74957 74,86713 76,90828 78,84783 80,65889 82,31322 83,78181 85,03555 86,04608 86,7868 87,2339 87,36758 87,17313 86,64199 85,77261 84,57102 83,05105 81,23412 79,1486 76,82879 74,31354 71,64461 68,86503 66,01736 63,14223 60,27707 57,45517 54,70512 52,05048 49,50986 47,09714 44,82189 42,68989 40,70374 38,86337 37,16665 35,60986 34,18816 32,89595 31,72717 30,67557 29,73492 28,89912 28,16235 27,51909. 6,651422 6,767201 6,900244 7,051329 7,221218 7,410626 7,620195 7,850444 8,101729 8,374184 8,667657 8,981649 9,315243 9,667043 10,03512 10,41695 10,80945 11,20893 11,61116 12,01146 12,40481 12,78601 13,14983 13,49124 13,80553 14,08856 14,33682 14,54761 14,71903 14,85004 14,94039 14,99062 15,0019 14,97597 14,91504 14,82162 14,69847 14,54848 14,37457 14,17967 13,96661 13,73813 13,49678 13,24499 12,98499 12,71881 12,44832 12,1752. Page 4.

(5) Sheet1. H'(t). P'(t). H(t+0.5) 48,75. P(t+0.5). H'(t+0.5). -2,5. 0. -2,36921. -0,03652. 46,3779 14,96299. -2,30173. -0,0542. -2,23002. -0,07074 44,14576 14,89168. -2,15947. -0,08718. -2,08605 -1,94032 -1,79528 -1,65287 -1,51452 -1,38125 -1,25372 -1,13229 -1,0171 -0,90811 -0,80512 -0,70786 -0,61596 -0,52904 -0,44666 -0,3684 -0,29381 -0,22247 -0,15396 -0,08788 -0,02385 0,038497 0,099502 0,159488 0,218761 0,277605 0,336287 0,395055 0,454138 0,51375 0,574083 0,635314 0,697596 0,761064 0,825829 0,891976 0,959564 1,028617 1,099127 1,171044 1,244272 1,318664 1,394011. -0,10238 -0,13122 -0,15716 -0,18018 -0,2003 -0,21762 -0,23227 -0,24439 -0,25416 -0,26175 -0,26736 -0,27116 -0,27333 -0,27404 -0,27345 -0,2717 -0,26894 -0,26528 -0,26085 -0,25574 -0,25005 -0,24385 -0,23722 -0,23023 -0,22293 -0,21537 -0,20759 -0,19963 -0,19151 -0,18326 -0,1749 -0,16644 -0,15789 -0,14926 -0,14056 -0,13177 -0,1229 -0,11395 -0,10489 -0,09571 -0,0864 -0,07694 -0,0673. -2,01404 -1,86818 -1,72408 -1,58341 -1,44738 -1,31682 -1,19224 -1,07388 -0,96176 -0,85576 -0,75566 -0,66111 -0,57174 -0,48713 -0,40686 -0,33049 -0,25757 -0,1877 -0,12046 -0,05545 0,00769 0,069321 0,129773 0,189362 0,248381 0,307107 0,365796 0,424689 0,484006 0,543949 0,604705 0,666437 0,729292 0,793391 0,858834 0,925693 0,99401 1,063795 1,135019 1,207611 1,28145 1,35636 1,432102. -0,11745 -0,14485 -0,16933 -0,19088 -0,20958 -0,22553 -0,23888 -0,24978 -0,25842 -0,26498 -0,26965 -0,2726 -0,274 -0,27403 -0,27283 -0,27054 -0,26731 -0,26324 -0,25845 -0,25303 -0,24707 -0,24064 -0,23382 -0,22667 -0,21923 -0,21155 -0,20367 -0,19563 -0,18744 -0,17913 -0,17071 -0,16221 -0,15362 -0,14496 -0,13621 -0,12739 -0,11848 -0,10947 -0,10036 -0,09112 -0,08174 -0,07219 -0,06246. 42,05828 40,1171 38,32144 36,66857 35,15433 33,77359 32,52053 31,389 30,37272 29,46546 28,66119 27,95417 27,33901 26,81074 26,3648 25,99707 25,70388 25,48197 25,32853 25,24111 25,21767 25,25654 25,35636 25,51612 25,73512 26,01293 26,34937 26,74455 27,19878 27,7126 28,28671 28,92203 29,61961 30,38064 31,20641 32,09832 33,0578 34,08634 35,18539 36,35637 37,60059 38,91924 40,31327. 15. 14,78869 14,65682 14,49899 14,31816 14,11721 13,89897 13,66612 13,42118 13,16652 12,9043 12,63651 12,36496 12,09128 11,81692 11,5432 11,27124 11,00208 10,7366 10,47558 10,21969 9,969504 9,725534 9,488203 9,257875 9,034856 8,819407 8,611745 8,412054 8,220488 8,037177 7,86223 7,695745 7,537808 7,388498 7,247893 7,116071 6,993115 6,879116 6,774174 6,678406 6,591943 6,514937 6,447566. -2,4375. P'(t+0.5) -0,01875. Page 5.

(6) Sheet1. 1,470041 1,546403 1,622664 1,698292 1,772654 1,844995 1,914437 1,97996 2,040398 2,094428 2,140569 2,177175 2,202444 2,214431 2,211064 2,190181 2,149576 2,087061 2,000548 1,888148 1,748291 1,579862 1,382351 1,156002 0,901963 0,62241 0,320636 0,001078 -0,33072 -0,66826 -1,00428 -1,3311 -1,64098 -1,92659 -2,18136 -2,39993 -2,57841 -2,71455 -2,80781 -2,85926 -2,87135 -2,84769 -2,79265 -2,71108 -2,60798 -2,48822 -2,35635 -2,21647 -2,07214 -1,92631 -1,78141 -1,63929. -0,05746 -0,04739 -0,03705 -0,02641 -0,01544 -0,00408 0,007692 0,019937 0,032698 0,046023 0,059959 0,074553 0,089847 0,105876 0,122667 0,140234 0,158572 0,177654 0,197422 0,217784 0,238602 0,259688 0,280795 0,301615 0,32177 0,340819 0,358259 0,373537 0,386071 0,395268 0,400564 0,40145 0,397517 0,388485 0,374237 0,354835 0,330527 0,301741 0,269063 0,233203 0,194956 0,155159 0,114642 0,074197 0,034541 -0,0037 -0,04002 -0,07402 -0,10539 -0,13396 -0,15962 -0,18235. 41,78339 43,32994 44,95283 46,65146 48,42458 50,2702 52,18543 54,16639 56,20803 58,30397 60,44636 62,6257 64,83068 67,04805 69,26248 71,45649 73,61035 75,70216 77,70789 79,60162 81,35582 82,94183 84,33043 85,49263 86,40056 87,02847 87,35392 87,35889 87,03091 86,36405 85,35967 84,02689 82,38265 80,45131 78,26386 75,85675 73,27037 70,54738 67,73101 64,86337 61,9841 59,12916 56,33008 53,61347 51,00091 48,50902 46,14985 43,93134 41,85783 39,93071 38,14897 36,50971. 6,390031 6,342563 6,305426 6,27892 6,263382 6,259191 6,26677 6,286589 6,319161 6,365053 6,424877 6,49929 6,588995 6,694729 6,817257 6,957357 7,115807 7,293354 7,490694 7,708426 7,947017 8,206745 8,487644 8,789438 9,111476 9,452663 9,811401 10,18553 10,57232 10,96842 11,36993 11,77241 12,17102 12,56063 12,936 13,29192 13,62345 13,92608 14,19588 14,42966 14,62501 14,78038 14,89505 14,96912 15,00338 14,99928 14,95875 14,88416 14,77815 14,64354 14,48326 14,30025. 1,508367 1,584765 1,660816 1,735938 1,809442 1,880512 1,948202 2,011421 2,068927 2,119318 2,161032 2,192344 2,211378 2,21612 2,204447 2,174166 2,123065 2,048989 1,949929 1,82413 1,670221 1,487359 1,275377 1,034941 0,76769 0,476339 0,164749 -0,16208 -0,4981 -0,83637 -1,16936 -1,4893 -1,78854 -2,06006 -2,29782 -2,49714 -2,65491 -2,76975 -2,84191 -2,87323 -2,86677 -2,8266 -2,75739 -2,66412 -2,55177 -2,4251 -2,28846 -2,14568 -2,00003 -1,8542 -1,71032 -1,57001. -0,0525 -0,04231 -0,03182 -0,02103 -0,00987 0,001691 0,013696 0,026192 0,03923 0,052855 0,067117 0,082058 0,097719 0,114132 0,131317 0,14928 0,168007 0,187455 0,207551 0,228182 0,249185 0,270345 0,291384 0,31196 0,331663 0,350018 0,366494 0,38052 0,391503 0,398856 0,402037 0,400578 0,39413 0,382488 0,365621 0,343686 0,317023 0,286144 0,251707 0,214473 0,175268 0,134932 0,094287 0,054091 0,015017 -0,02236 -0,05759 -0,09033 -0,12033 -0,14745 -0,17164 -0,19291. Page 6.

(7) Sheet1. -1,50136 -1,36859 -1,24162 -1,12077 -1,00618 -0,89777 -0,79534 -0,69861 -0,60721 -0,52074 -0,43879 -0,3609 -0,28665 -0,2156 -0,14735 -0,08149 -0,01764 0,044561 0,105451 0,165354 0,224572 0,283389 0,342069 0,400858 0,459985 0,519661 0,580078 0,641407 0,703804 0,767399 0,832302 0,898595 0,966333 1,03554 1,106202 1,178264 1,251627 1,326137 1,401582 1,47768 1,554074 1,630321 1,70588 1,780107 1,852235 1,921371 1,986484 2,046391 2,099754 2,145074 2,18069 2,204786. -0,2022 -0,21925 -0,23364 -0,24552 -0,25507 -0,26246 -0,26788 -0,27151 -0,27353 -0,2741 -0,27339 -0,27153 -0,26867 -0,26493 -0,26042 -0,25525 -0,2495 -0,24326 -0,23659 -0,22957 -0,22224 -0,21465 -0,20685 -0,19887 -0,19073 -0,18247 -0,17409 -0,16562 -0,15707 -0,14843 -0,13972 -0,13093 -0,12205 -0,11308 -0,10401 -0,09482 -0,0855 -0,07602 -0,06636 -0,0565 -0,0464 -0,03603 -0,02537 -0,01436 -0,00296 0,008859 0,021153 0,033967 0,047351 0,061351 0,076013 0,091379. 35,00866 33,6406 32,39966 31,27965 30,2743 29,37739 28,5829 27,88512 27,27871 26,75872 26,32065 25,96041 25,67437 25,45933 25,31249 25,23146 25,21423 25,25915 25,36492 25,53055 25,75536 26,03894 26,38116 26,78214 27,24222 27,76194 28,34205 28,98346 29,68724 30,4546 31,28685 32,18537 33,15163 34,18709 35,29321 36,47141 37,72299 39,04911 40,45072 41,92848 43,48271 45,11327 46,8195 48,60009 50,45295 52,37514 54,36265 56,41031 58,5116 60,65853 62,84141 65,04877. 14,09741 13,87755 13,64332 13,39725 13,14168 12,87876 12,61045 12,33856 12,06468 11,79027 11,51661 11,24483 10,97594 10,71081 10,45021 10,19481 9,945175 9,701798 9,4651 9,23544 9,013118 8,798391 8,591473 8,392544 8,201755 8,019233 7,845088 7,679414 7,522298 7,373817 7,23405 7,103074 6,980974 6,867841 6,763776 6,668897 6,583338 6,507254 6,440822 6,384249 6,337767 6,301644 6,276184 6,261727 6,258658 6,267404 6,288437 6,322278 6,369498 6,430712 6,506585 6,597822. -1,43445 -1,30443 -1,18042 -1,06265 -0,95112 -0,8457 -0,74614 -0,65211 -0,56322 -0,47905 -0,39918 -0,32316 -0,25057 -0,18097 -0,11396 -0,04915 0,013824 0,075323 0,135677 0,195196 0,254175 0,312886 0,371586 0,430511 0,489882 0,549899 0,610746 0,672586 0,735561 0,799794 0,865379 0,932386 1,000856 1,070794 1,142167 1,2149 1,288867 1,363886 1,439713 1,51603 1,592438 1,668449 1,743472 1,816804 1,887617 1,954953 2,017704 2,074614 2,124265 2,165077 2,195311 2,213075. -0,21134 -0,22703 -0,24013 -0,2508 -0,25923 -0,26559 -0,27008 -0,27287 -0,27413 -0,27402 -0,27271 -0,27032 -0,267 -0,26285 -0,25799 -0,25251 -0,2465 -0,24003 -0,23317 -0,22599 -0,21852 -0,21082 -0,20292 -0,19486 -0,18665 -0,17833 -0,16991 -0,16139 -0,1528 -0,14412 -0,13537 -0,12654 -0,11762 -0,1086 -0,09947 -0,09022 -0,08082 -0,07126 -0,06151 -0,05153 -0,04131 -0,03079 -0,01996 -0,00877 0,002835 0,014886 0,027434 0,040528 0,054215 0,068542 0,083554 0,099289. Page 7.

(8) Sheet1. 2,215401 2,210452 2,18777 2,145145 2,080394 1,991443 1,876425 1,733808 1,562528 1,362138 1,132965 0,876251 0,594279 0,290451 -0,03068 -0,36347 -0,70133 -1,03693 -1,36257 -1,67054 -1,95353 -2,20509 -2,41998 -2,59446 -2,72646 -2,81558 -2,86306 -2,87146 -2,84449 -2,7866 -2,70265 -2,59764 -2,47643 -2,34354 -2,20301 -2,05835 -1,91245 -1,76769 -1,62588 -1,48837 -1,35611 -1,22969 -1,10943 -0,99542 -0,88758 -0,78571 -0,6895 -0,59859. 0,107483 0,124353 0,141999 0,160415 0,179571 0,199407 0,219826 0,240686 0,261793 0,282895 0,303676 0,323753 0,342678 0,359942 0,374988 0,387231 0,39608 0,400973 0,40141 0,396991 0,387453 0,372694 0,352794 0,32802 0,298815 0,265781 0,229638 0,191188 0,151268 0,11071 0,070296 0,030738 -0,00735 -0,04347 -0,07723 -0,10835 -0,13664 -0,16202 -0,18447 -0,20405 -0,22084 -0,23498 -0,24662 -0,25595 -0,26314 -0,26838 -0,27184 -0,27371. 67,26716 69,48102 71,67266 73,82214 75,90733 77,904 79,78604 81,52579 83,09448 84,46288 85,60203 86,48421 87,08394 87,37913 87,35224 86,99139 86,29132 85,25414 83,88973 82,21578 80,25736 78,04606 75,6188 73,01631 70,28138 67,45723 64,58583 61,70649 58,85482 56,06188 53,3538 50,75166 48,27164 45,92537 43,72038 41,66072 39,74751 37,97953 36,35371 34,86567 33,51011 32,2811 31,17245 30,17786 29,29113 28,50627 27,81759 27,2198. 6,705163 6,829377 6,971243 7,131537 7,311003 7,51033 7,730108 7,970787 8,232626 8,515631 8,819495 9,143526 9,486582 9,847014 10,22261 10,61057 11,00749 11,40942 11,81186 12,20996 12,59854 12,97236 13,32623 13,65525 13,95494 14,22145 14,45164 14,64321 14,79467 14,90539 14,97554 15,00599 14,99822 14,95424 14,87642 14,76745 14,63015 14,46747 14,28233 14,07765 13,8562 13,62064 13,37347 13,11702 12,85342 12,58462 12,3124 12,03834. 2,216343 2,202981 2,170791 2,117561 2,041145 1,939552 1,811057 1,654332 1,46859 1,25374 1,010536 0,740715 0,447104 0,133678 -0,19445 -0,53114 -0,86938 -1,20159 -1,51997 -1,81693 -2,08552 -2,31981 -2,51526 -2,66893 -2,77959 -2,84767 -2,87513 -2,86516 -2,82189 -2,75005 -2,65464 -2,54062 -2,41272 -2,27525 -2,13199 -1,98615 -1,84037 -1,69672 -1,55679 -1,4217 -1,29222 -1,16878 -1,05159 -0,94065 -0,8358 -0,73678 -0,64325 -0,55483. 0,115779 0,133043 0,151085 0,169888 0,189409 0,209568 0,230249 0,251285 0,272454 0,293473 0,313992 0,333594 0,3518 0,368073 0,381837 0,3925 0,399476 0,402229 0,400301 0,393353 0,381199 0,363824 0,341402 0,314293 0,283025 0,248267 0,210789 0,171421 0,131004 0,090355 0,050225 0,011279 -0,02592 -0,06093 -0,09342 -0,12315 -0,15 -0,17391 -0,1949 -0,21306 -0,22849 -0,24134 -0,25179 -0,26001 -0,26618 -0,27049 -0,27312 -0,27424. Page 8.

(9)