<simulation>
<header>
<title lang="french">Cinétique de prédation de proies par des prédateurs</title>
<title lang="english">Kinetics of prey predation by predators</title>
<title lang="spanish">Cinética de depredación de presas por depredadores </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 proies et de prédateurs</p>
</notes>
<notes lang="english">
<p>This simulation aims to illustrate the kinetics of predation of preys by predators, 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 presas y depredadores.</p>
</notes>
<parameters><section>
<title lang="french">Paramètres cinétiques</title>
<title lang="english">Kinetic parameters</title>
<title lang="spanish">Para metros 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 proies sans prédateur (jour-1)</name><name lang="english">r, Growth rate of preys without predator (day-1)</name><name lang="spanish">Velocidad de reproducción de las presas sin depredador (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 proies, sans prédateur (jour-1)</name><name lang="english">k, Mortality of prey, without predator (day-1)</name><name lang="spanish">k, Mortalidad de las presas, sin depredador (jour-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 proies par prédateur (prédateur-1 jour-1)</name><name lang="english">a, Predation rate of prey, per number of predator (predator-1 day-1)</name><name lang="spanish">a, Velocidad de captura de las presas por depredador (depredador-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 prédateurs, par nombre de proies capturées (proie-1 jour-1)</name><name lang="english">b, Growth rate of predators, per number of eaten prey (prey-1 day-1)</name><name lang="spanish">b, Velocidad de reproducción de los depredadores, por numero de presas capturadas (presa-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 prédateurs, sans proie (jour-1)</name><name lang="english">q, Mortality of predators, without prey (day-1)</name><name lang="spanish">q, Mortalidad de los depredadores, sin presa (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="Prey0" max="10000" min="0" state="normal" unit=""><name lang="french">Concentration initiale en proie (animal par km2)</name><name lang="english">Initial concentration of prey (animal per square km)</name><name lang="spanish">Concentración inicial en presa (animal por km²)</name><value>5000</value></scalar>
<scalar increment="50" label="Predator0" max="1000" min="1" state="normal" unit=""><name lang="french">Concentration initiale en prédateur (animal par km2)</name><name lang="english">Initial concentration of predator (animal per square km)</name><name lang="spanish">Concentración inicial en depredador (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="Prey" size="1" unit="">
<name lang="french">Concentration en proie (km-2)</name>
<name lang="english">Prey concentration (km-2)</name>
<name lang="spanish">Concentración en presa (km-2)</name>
<derivative>(r*Prey) - (k*Prey) - (a*Prey*Predator)</derivative>
<initialcondition>Prey0</initialcondition>
</state>
<state label="Predator" size="1">
<name lang="french">Concentration en prédateur (km-2)</name>
<name lang="english">Predator concentration (km-2)</name>
<name lang="spanish">Concentración en depredador (km-2)</name>
<derivative>(b*Prey*Predator) - (q*Predator)</derivative>
<initialcondition>Predator0</initialcondition>
</state>
</states>
</ode>
</compute>
<graphs>
<parametriccurve2d label="Prey_vs_predator">
<name lang="french">Portrait de phase</name>
<name lang="english">Phase picture</name>
<name lang="spanish">Imagen de fase</name>
<x1>
<name lang="french">Proie</name>
<name lang="english">Prey</name>
<name lang="spanish">Presa</name>
<value>Prey</value>
</x1>
<x2>
<name lang="french">Prédateur</name>
<name lang="english">Predator</name>
<name lang="spanish">Depredador</name>
<value>Predator</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="Prey" thickness="2" />
<drawcurve2d color="green" ref="Predator" thickness="2" />
</axis2d>
<axis2d>
<drawcurve2d ref="Prey_vs_predator" />
</axis2d>
</window>
</display>
<save>
<file format="csv" href="essai.csv" labels="r k a b q time Prey Predator" />
</save>
</simulation>