<simulation>
<header>
<title lang="french">Cinétique de prédation de lapins par des renards</title>
<title lang="english">Kinetics of rabbit predation by foxes</title>
<title lang="spanish">Cinética de depredación de conejos por zorros</title>
<author>Pauss André, Mottelet Stéphane, Guillaume Barbaud, UTC</author>
<date> August 25th, 2005 </date>
<keywords>simulation, scilab, xml, Lotka-Voltera</keywords>
<keywords lang="spanish">Simulación, scilab, xml, Lotka-Voltera</keywords>
<image href="Lotka-Voltera.gif" />
</header>
<notes lang="french">
<p>Cette simulation a pour objet d'illustrer l'équation de Lotka-Voltera qui décrit la dynamique des populations de lapins et de renards</p>
</notes>
<notes lang="english">
<p>This simulation aims to illustrate the kinetics of predation of rabbits by foxes, with the Lotka-Voltera expression</p>
</notes>
<notes lang="spanish">
<p>Esta simulación tiene como objeto de ilustrar la ecuación de Lotka-Voltera que describe la dinámica de las poblaciones de conejos y zorros</p>
</notes>
<parameters><section>
<title lang="french">Paramètres cinétiques</title>
<title lang="english">Kinetic parameters</title>
<title lang="spanish">Parámetros cinéticos</title>
<scalar increment="0.1" label="r" max="10" min="0.5" state="normal" unit="d-1"><name lang="french">r, Vitesse de reproduction des lapins sans renard (jour-1)</name><name lang="english">r, Growth rate of rabbits without fox (day-1)</name><name lang="spanish">Velocidad de reproducción de los conejos sin zorro (dia-1)</name><value>2</value></scalar>
<scalar increment="0.01" label="k" max="3" min="0.0001" state="normal" unit="d-1"><name lang="french">k, Mortalité des lapins, sans renard (jour-1)</name><name lang="english">k, Mortality of rabbit, without fox (day-1)</name><name lang="spanish">k, Mortalidad de los conejos, sin zorro (dia -1)</name><value>0.01</value></scalar>
<scalar increment="0.001" label="a" max="0.01" min="0.001" state="normal" unit=""><name lang="french">a, Vitesse de capture des lapins par renard (renard-1 jour-1)</name><name lang="english">a, Predation rate of rabbit, per number of fox (fox-1 day-1)</name><name lang="spanish">a, Velocidad de captura de conejos por zorro (zorro-1 dia-1)</name><value>0.001</value></scalar>
<scalar increment="0.0005" label="b" max="0.01" min="0.001" state="normal" unit=""><name lang="french">b, Vitesse de reproduction des renards, par nombre de lapins capturés (lapin-1 jour-1)</name><name lang="english">b, Growth rate of foxes, per number of eaten rabbit (rabbit-1 day-1)</name><name lang="spanish">b, Velocidad de reproducción de zorros por numero de conejos capturados (conejo-1 dia-1)</name><value>0.002</value></scalar>
<scalar increment="0.5" label="q" max="20" min="0.5" state="normal" unit="d-1"><name lang="french">q, Mortalité des renards, sans lapin (jour-1)</name><name lang="english">q, Mortality of foxes, without rabbit (day-1)</name><name lang="spanish">q, Mortalidad de los zorros, sin conejo (dia -1)</name><value>10</value></scalar>
</section><section>
<title lang="french">Concentrations initiales</title>
<title lang="english">Initial concentrations</title>
<title lang="spanish">Concentraciones iníciales</title>
<scalar increment="1000" label="rabbit0" max="10000" min="0" state="normal" unit=""><name lang="french">Concentration initiale en lapin (animal par km2)</name><name lang="english">Initial concentration of rabbit (animal per square km)</name><name lang="spanish">Concentración inicial en conejo (animal por km²)</name><value>5000</value></scalar>
<scalar increment="50" label="fox0" max="1000" min="1" state="normal" unit=""><name lang="french">Concentration initiale en renard (animal par km2)</name><name lang="english">Initial concentration of fox (animal per square km)</name><name lang="spanish">Concentración inicial en zorro (animal por km²)</name><value>100</value></scalar>
</section><section>
<title lang="french">Temps de simulation</title>
<title lang="english">Simulation duration</title>
<title lang="spanish">Tiempo de simulación</title>
<scalar increment="1" label="final_time" max="200" min="0.001" state="normal" unit="d"><name lang="french">Temps final (jour)</name><name lang="english">Final time (day)</name><name lang="spanish">Tiempo final (dia)</name><value>10</value></scalar>
</section></parameters>
<compute>
<defdomain1d label="time" unit="d">
<name lang="french">Temps</name>
<name lang="english">Time</name>
<name lang="spanish">Tiempo</name>
<interval discretization="linear" steps="1000">
<initialvalue>0</initialvalue>
<finalvalue>final_time</finalvalue>
</interval>
</defdomain1d>
<ode label="predation">
<refdomain1d ref="time" />
<states>
<state label="rabbit" size="1" unit="">
<name lang="french">Concentration en lapin (km-2)</name>
<name lang="english">rabbit concentration (km-2)</name>
<name lang="spanish">Concentración en conejo (km-2)</name>
<derivative>(r*rabbit) - (k*rabbit) - (a*rabbit*fox)</derivative>
<initialcondition>rabbit0</initialcondition>
</state>
<state label="fox" size="1">
<name lang="french">Concentration en renard (km-2)</name>
<name lang="english">Fox concentration (km-2)</name>
<name lang="spanish">Concentración en zoroo (km-2)</name>
<derivative>(b*rabbit*fox) - (q*fox)</derivative>
<initialcondition>fox0</initialcondition>
</state>
</states>
</ode>
</compute>
<graphs>
<parametriccurve2d label="rabbit_vs_fox">
<name lang="french">Portrait de phase</name>
<name lang="english">Phase picture</name>
<name lang="spanish">Imagen de fase</name>
<x1>
<name lang="french">Lapin</name>
<name lang="english">rabbit</name>
<name lang="spanish">Conejo</name>
<value>rabbit</value>
</x1>
<x2>
<name lang="french">Renard</name>
<name lang="english">Fox</name>
<name lang="spanish">Zorro</name>
<value>fox</value>
</x2>
</parametriccurve2d>
</graphs>
<display>
<window splitx="1" splity="2">
<title lang="french">Résultats</title>
<title lang="english">Results</title>
<title lang="spanish">Resultados</title>
<axis2d>
<drawcurve2d color="red" ref="rabbit" thickness="2" />
<drawcurve2d color="green" ref="fox" thickness="2" />
</axis2d>
<axis2d>
<drawcurve2d ref="rabbit_vs_fox" />
</axis2d>
</window>
</display>
<save>
<file format="csv" href="essai.csv" labels="r k a b q time rabbit fox" />
</save>
</simulation>