<html>  <head>   <title>chaos.xml</title>   <link rel="stylesheet" type="text/css" href="/syracuse/xml-brut.css">  </head> <body bgcolor="#FFFFFF"> Voici le source du fichier <strong>XML</strong> demand.<br> <h1>chaos.xml</h1> <span class="entetexml">&lt;?xml version="1.0" encoding="ISO-8859-1"  ?&gt;</span><br> <br><span class="element">&lt;pPbbgraf&gt;</span> <br>&nbsp;&nbsp;<span class="element">&lt;entete&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;dossier&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">chaos</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/dossier&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">La fonction logistique</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;auteur&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">Jean-Michel Sarlat</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/auteur&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;intro&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">Cette fonction modlise quelques situations d'quilibre, on la retrouve en particulier dans les systmes proies-prdateurs</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/intro&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;par&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">La fonction </span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;emph&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">logistique</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/emph&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata"> est dfinie par :</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;br&gt;</span><span class="element">&lt;/br&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;texte</span><span class="nom"> f =</span><span class="valeur"> "tex"</span> <span class="nom"> n =</span><span class="valeur"> "t1"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">$$f_{a}: x \mapsto a x (1-x)$$</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/texte&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata"> Tant que le paramtre </span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;strong&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/strong&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata"> est compris entre 0 et 4, l'intervalle [0,1] est stable et l'on peut observer les diffrentes itrations. Le dterminisme est assur pour les valeurs de </span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;strong&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/strong&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata"> proche de 0, le chaos apparat lorsqu'il crot.</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/par&gt;</span> <br>&nbsp;&nbsp;<span class="element">&lt;/entete&gt;</span> <br>&nbsp;&nbsp;<span class="element">&lt;corps&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a = 4</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-0.1,1.1,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique01"</span> <span class="nom"> physique =</span><span class="valeur"> "300,300"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet</span><span class="nom"> couleur =</span><span class="valeur"> "bleu"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">iterations(4*x*(1-x),x=-0.1..1.1,0.32,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-1,31,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique01-evo"</span> <span class="nom"> physique =</span><span class="valeur"> "500,250"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">dynamique(4*x*(1-x),x=-0.1..1.1,0.32,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a = 3.5</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-0.1,1.1,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique04"</span> <span class="nom"> physique =</span><span class="valeur"> "300,300"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet</span><span class="nom"> couleur =</span><span class="valeur"> "orange"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">iterations(3.5*x*(1-x),x=-0.1..1.1,0.32,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-1,31,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique04-evo"</span> <span class="nom"> physique =</span><span class="valeur"> "500,250"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">dynamique(3.5*x*(1-x),x=-0.1..1.1,0.32,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a = 3</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-0.1,1.1,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique02"</span> <span class="nom"> physique =</span><span class="valeur"> "300,300"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet</span><span class="nom"> couleur =</span><span class="valeur"> "bleu"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">iterations(3*x*(1-x),x=-0.1..1.1,0.32,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-1,31,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique02-evo"</span> <span class="nom"> physique =</span><span class="valeur"> "500,250"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">dynamique(3*x*(1-x),x=-0.1..1.1,0.32,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a = 2.5</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-0.1,1.1,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique05"</span> <span class="nom"> physique =</span><span class="valeur"> "300,300"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet</span><span class="nom"> couleur =</span><span class="valeur"> "bleu"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">iterations(2.5*x*(1-x),x=-0.1..1.1,0.1,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-1,31,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique05-evo"</span> <span class="nom"> physique =</span><span class="valeur"> "500,250"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">dynamique(2.5*x*(1-x),x=-0.1..1.1,0.1,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a = 2</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-0.1,1.1,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique06"</span> <span class="nom"> physique =</span><span class="valeur"> "300,300"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet</span><span class="nom"> couleur =</span><span class="valeur"> "bleu"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">iterations(2*x*(1-x),x=-0.1..1.1,0.1,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-1,31,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique06-evo"</span> <span class="nom"> physique =</span><span class="valeur"> "500,250"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">dynamique(2*x*(1-x),x=-0.1..1.1,0.1,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;section&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">a = 1.5</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/titre&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-0.1,1.1,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique07"</span> <span class="nom"> physique =</span><span class="valeur"> "300,300"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet</span><span class="nom"> couleur =</span><span class="valeur"> "rose"</span> <span class="nom"> trait =</span><span class="valeur"> "continu"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">iterations(1.5*x*(1-x),x=-0.1..1.1,0.1,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;figure</span><span class="nom"> logique =</span><span class="valeur"> "-1,31,-0.1,1.1"</span> <span class="nom"> nom =</span><span class="valeur"> "logistique07-evo"</span> <span class="nom"> physique =</span><span class="valeur"> "500,250"</span> <span class="element">&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="pcdata">dynamique(1.5*x*(1-x),x=-0.1..1.1,0.1,30)</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/objet&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/figure&gt;</span> <br>&nbsp;&nbsp;&nbsp;&nbsp;<span class="element">&lt;/section&gt;</span> <br>&nbsp;&nbsp;<span class="element">&lt;/corps&gt;</span> <br><span class="element">&lt;/pPbbgraf&gt;</span><hr> <i>Compos par <a href="http://melusine.eu.org/syracuse/xml/pP/">petitParseur</a> le samedi 26 avril 2003 </i> </body> </html> 
