A Predator-Prey Model in the Chemostat with Time Delay

<table>The periodic solution disappears at the secondary Hopf bifurcation at <svg height="19.200001" id="M918" style="vertical-align:-4.35121pt" version="1.1" viewbox="0 0 60.962502 19.200001" width="60.962502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.2)">
<g transform="translate(72,-56.64)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.55,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
<tspan style="font-size: 8.75px; " x="0" y="9.21">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.2,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">≈</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">8</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.6875" id="M919" style="vertical-align:-3.49493pt" version="1.1" viewbox="0 0 19.4 14.6875" width="19.4" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6875)">
<g transform="translate(72,-60.25)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.02,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">+</tspan>
</text>
</g>
</g>
</svg> regains stability. In this figure <svg height="19.200001" id="M920" style="vertical-align:-4.35121pt" version="1.1" viewbox="0 0 80.537498 19.200001" width="80.537498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.2)">
<g transform="translate(72,-56.64)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan>
<tspan style="font-size: 12.50px; " x="9.8648672" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.905256" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.156755" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.282507" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="41.009838" y="0">&gt;</tspan>
<tspan style="font-size: 12.50px; " x="53.050228" y="0">𝜏</tspan>
</text>
<text transform="matrix(1,0,0,-1,-12.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
<tspan style="font-size: 8.75px; " x="0" y="9.21">0</tspan>
</text>
</g>
</g>
</svg>. The other parameters are the same as for Figure <a href="../fig4/">4</a>.</table>

International Journal of Differential Equations

A Predator-Prey Model in the Chemostat with Time Delay

Figure 11