The Analysis and Control for Singular Ecological-Economic Model with Harvesting and Migration

<table>The state response of <svg height="10.925" id="M259" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
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<text transform="matrix(1,0,0,-1,-65.07,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
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</svg>, <svg height="10.925" id="M260" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg>, and <svg height="10.325" id="M261" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.225 10.325" width="12.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
</text>
</g>
</g>
</svg> when <svg height="11.1" id="M262" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 61.862499 11.1" width="61.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
<tspan style="font-size: 12.50px; " x="12.340461" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.38085" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="30.632351" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="36.88385" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="43.135349" y="0">5</tspan>
</text>
</g>
</g>
</svg> with the controller <svg height="7.1624999" id="M263" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑢</tspan>
</text>
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</svg>.</table>

Journal of Applied Mathematics

fig2

Figure 2

Figure 2: The Analysis and Control for Singular Ecological-Economic Model with Harvesting and Migration 