Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy

<table>(a) A period <svg height="10.325" id="M265" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg">
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<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">𝑇</tspan>
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</svg> attractor when <svg height="10.9125" id="M266" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 43.737499 10.9125" width="43.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
<tspan style="font-size: 12.50px; " x="10.339981" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.380369" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.63187" y="0">0</tspan>
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</svg>, (b) time series algae population when <svg height="10.9125" id="M267" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 43.737499 10.9125" width="43.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
<tspan style="font-size: 12.50px; " x="10.339981" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.380369" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.63187" y="0">0</tspan>
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</svg>.</table>

Discrete Dynamics in Nature and Society

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Figure 2

Figure 2: Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy 