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danielvartan committed Oct 25, 2024
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2 changes: 1 addition & 1 deletion docs/index.html
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Expand Up @@ -180,7 +180,7 @@ <h1 class="title">Lotka-Volterra’s Predator–Prey Model</h1>

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<section id="overview" class="level2"><h2 class="anchored" data-anchor-id="overview">Overview</h2>
<p>This document focuses on representing the <a href="https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations">Lotka-Volterra’s model</a>, originally developed by Alfred J. Lotka <span class="citation" data-cites="lotka1925">(<a href="#ref-lotka1925" role="doc-biblioref">1925</a>)</span> and Vito Volterra <span class="citation" data-cites="volterra1926">(<a href="#ref-volterra1926" role="doc-biblioref">1926</a>)</span>, to describe the dynamics of biological systems where two species interact: one as a predator and the other as prey.</p>
<p>This document focuses on illustrating the <a href="https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations">Lotka-Volterra’s model</a>, originally developed by Alfred J. Lotka <span class="citation" data-cites="lotka1925">(<a href="#ref-lotka1925" role="doc-biblioref">1925</a>)</span> and Vito Volterra <span class="citation" data-cites="volterra1926">(<a href="#ref-volterra1926" role="doc-biblioref">1926</a>)</span>, to describe the dynamics of biological systems where two species interact: one as a predator and the other as prey.</p>
<p>The dynamics of the model are represented by the following set of first-order, nonlinear differential equations:</p>
<p><span class="math display">\[
\begin{aligned}
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2 changes: 1 addition & 1 deletion docs/search.json
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"href": "index.html#overview",
"title": "Lotka-Volterra’s Predator–Prey Model",
"section": "Overview",
"text": "Overview\nThis document focuses on representing the Lotka-Volterra’s model, originally developed by Alfred J. Lotka (1925) and Vito Volterra (1926), to describe the dynamics of biological systems where two species interact: one as a predator and the other as prey.\nThe dynamics of the model are represented by the following set of first-order, nonlinear differential equations:\n\\[\n\\begin{aligned}\n\\frac{dx}{dt} & = \\alpha x - \\beta xy \\\\\n\\frac{dy}{dt} & = - \\gamma y + \\delta xy\n\\end{aligned}\n\\]\nwhere:\n\n\n\\(x\\) and \\(y\\) are the populations of the prey and predator, respectively;\n\n\\(\\alpha\\) and \\(\\delta\\) are the prey per capita growth rate and the effect of the presence of prey on the predator’s growth rate, respectively;\n\n\\(\\beta\\) and \\(\\gamma\\) are the effect of the presence of predators on the prey death rate and predator’s per capita death rate, respectively."
"text": "Overview\nThis document focuses on illustrating the Lotka-Volterra’s model, originally developed by Alfred J. Lotka (1925) and Vito Volterra (1926), to describe the dynamics of biological systems where two species interact: one as a predator and the other as prey.\nThe dynamics of the model are represented by the following set of first-order, nonlinear differential equations:\n\\[\n\\begin{aligned}\n\\frac{dx}{dt} & = \\alpha x - \\beta xy \\\\\n\\frac{dy}{dt} & = - \\gamma y + \\delta xy\n\\end{aligned}\n\\]\nwhere:\n\n\n\\(x\\) and \\(y\\) are the populations of the prey and predator, respectively;\n\n\\(\\alpha\\) and \\(\\delta\\) are the prey per capita growth rate and the effect of the presence of prey on the predator’s growth rate, respectively;\n\n\\(\\beta\\) and \\(\\gamma\\) are the effect of the presence of predators on the prey death rate and predator’s per capita death rate, respectively."
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2 changes: 1 addition & 1 deletion docs/sitemap.xml
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