{"id":252,"date":"2013-02-20T00:14:58","date_gmt":"2013-02-19T23:14:58","guid":{"rendered":"http:\/\/www.office-guru.com\/wordpress\/?p=252"},"modified":"2019-12-06T08:02:57","modified_gmt":"2019-12-06T07:02:57","slug":"matematica-ed-ecologia-le-equazioni-di-lotka-volterra","status":"publish","type":"post","link":"https:\/\/www.office-guru.com\/wordpress\/2013\/02\/matematica-ed-ecologia-le-equazioni-di-lotka-volterra\/","title":{"rendered":"Matematica ed Ecologia: le equazioni di Lotka-Volterra."},"content":{"rendered":"
\"Download<\/a><\/div>

Submitted by Flavio Bertamini<\/em>\u00a0<\/i>\u00a0<\/i>on Sat, 30\/05\/2009<\/em><\/p>\n

Mi sono divertito ad utilizzare Excel per fargli analizzare alcune equazioni che sono un classico negli studi di Analisi Matematica.<\/p>\n

Scherzosamente, possiamo immaginare un\u2019 isola con X lepri e Y volpi che interagiscono, si riproducono e muoiono.
\nL\u2019analisi di Volterra mostra che lungi dal rimanere stabile la popolazione generalmente evolve secondo leggi ben determinate percorrendo \u201corbite\u201d particolari come quella nella figura sottostante:<\/p>\n

\"Volterra\"<\/a><\/p>\n

Ai lettori meno preparati l\u2019invito a confrontare i risultati ottenuti con quelli della nota Wikipedia, mentre i pi\u00f9 smaliziati potranno notare che per ottenere risultati non banali con il personal computer si pu\u00f2 agire con un po\u2019 di fantasia senza necessitare obbligatoriamente dei pi\u00f9 famosi e blasonati software per il calcolo.
\nNel file .zip si trova pure un articolo con dettagli matematici pi\u00f9 approfonditi e qualche utile link.<\/p>\n

A tutti un invito a fornire critiche e suggerimenti<\/p>\n

VitoVolterra<\/a><\/p>\n

\n

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Submitted by Flavio Bertamini\u00a0\u00a0on Sat, 30\/05\/2009 Mi sono divertito ad utilizzare Excel per fargli analizzare alcune equazioni che sono un classico negli studi di Analisi Matematica. Scherzosamente, possiamo immaginare un\u2019 isola con X lepri e Y volpi che interagiscono, si … Continua a leggere→<\/span><\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"_links_to":"","_links_to_target":""},"categories":[5,15],"tags":[],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_shortlink":"https:\/\/wp.me\/p39IU1-44","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":256,"url":"https:\/\/www.office-guru.com\/wordpress\/2013\/02\/simulazione-di-un-ecosistema\/","url_meta":{"origin":252,"position":0},"title":"Simulazione di un Ecosistema","date":"20 Febbraio 2013","format":false,"excerpt":"Basandoci come stimolo sull'ottimo lavoro di Flavio, presentiamo qui una simulazione di ecosistema che emula le equazioni di Volterra: Le equazioni di Volterra sono facilmente simulabili con un piccolo programma che qui realizziamo in Excel che si ispira al famoso Wa-tor di Dewdney che ha pubblicato un interessante articolo su\u2026","rel":"","context":"In "Excel"","img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.office-guru.com\/wordpress\/wp-content\/uploads\/2013\/02\/wator_0-300x214.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1357,"url":"https:\/\/www.office-guru.com\/wordpress\/2014\/10\/regressioni-lineari-e-logaritmiche\/","url_meta":{"origin":252,"position":1},"title":"Regressioni lineari e logaritmiche","date":"15 Ottobre 2014","format":false,"excerpt":"Nei processi di pianificazione e controllo, o come si dice in inglese di Financial Planning (FP&A) capita di dover modellizzareil comportamento dei clienti rispetto a un servizio. Immaginiamo il comportamento tipico di un cliente che usufruisce di un servizo. All'inizio \u00e8 entusiasta e lo sua moltissimo (diciamo il massimo delle\u2026","rel":"","context":"In "Excel"","img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.office-guru.com\/wordpress\/wp-content\/uploads\/2014\/10\/regressioni2.gif?fit=455%2C275&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1024,"url":"https:\/\/www.office-guru.com\/wordpress\/2014\/02\/raccordare-due-punti-curva-a-piacere\/","url_meta":{"origin":252,"position":2},"title":"Come raccordare due punti con una curva a piacere","date":"7 Febbraio 2014","format":false,"excerpt":"[latexpage]Con questo articolo vorrei continuare a proporre qualche trucco per gli analisti finanziari come ho gi\u00e0 fatto in questo articolo. Lo scenario \u00e8 il seguente:spesso capita che le ipotesi del management siano diquesto tipo: Il parametro (KPI) xyz deve valere 100 il primo mese e deve scendere 60 in 12\u2026","rel":"","context":"In "Excel"","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":245,"url":"https:\/\/www.office-guru.com\/wordpress\/2013\/02\/matematica-scomposizione-in-fattori-primi\/","url_meta":{"origin":252,"position":3},"title":"Matematica – Scomposizione in fattori primi","date":"20 Febbraio 2013","format":false,"excerpt":"Flavio Bertamini ci ha mandato questo file che permette di lavorare con i numeri primi: Permette infatti di: Elencare i primi N numeri primi Scomporre un numero qualisasi in fattori primi La seconda ovviamente \u00e8 una procedura ben pi\u00f9 complicata della prima. Il file \u00e8 ben fatto e quindi rinnoviamo\u2026","rel":"","context":"In "Excel"","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1013,"url":"https:\/\/www.office-guru.com\/wordpress\/2014\/02\/modificare-velocemente-una-curva-di-penetrazione-senza-modificarne-la-forma\/","url_meta":{"origin":252,"position":4},"title":"Modificare velocemente una curva di penetrazione senza modificarne la forma","date":"5 Febbraio 2014","format":false,"excerpt":"Nella pianificazione finanziaria e nel Business Planning in generale si effettuano delle simulazioni relativamente alla capacita' di un certo prodotto\/servizio di entrare sul mercato e di acquisire una certa marketshare. Tipicamente la marketshare di un prodotto\/servizio segue una curva ad S come quella di qui sotto rappresentata: Dove l'ingresso sul\u2026","rel":"","context":"In "Excel"","img":{"alt_text":"curva S stirata","src":"https:\/\/i2.wp.com\/www.office-guru.com\/wordpress\/wp-content\/uploads\/2014\/02\/curva-S-stirata.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":963,"url":"https:\/\/www.office-guru.com\/wordpress\/2014\/02\/un-vero-mago-nei-calcoli\/","url_meta":{"origin":252,"position":5},"title":"Un vero mago nei calcoli…","date":"3 Febbraio 2014","format":false,"excerpt":"Certe volte usiamo Excel per fare semplici moltiplicazioni.. ecco qualcuno che non ne ha bisogno... La performance di Arthur Benjamin e' davvero impressionante... basta avere metodo!","rel":"","context":"In "Matematica"","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/posts\/252"}],"collection":[{"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/comments?post=252"}],"version-history":[{"count":5,"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/posts\/252\/revisions"}],"predecessor-version":[{"id":2040,"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/posts\/252\/revisions\/2040"}],"wp:attachment":[{"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/media?parent=252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/categories?post=252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.office-guru.com\/wordpress\/wp-json\/wp\/v2\/tags?post=252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}