Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control

<table>Periodic solutions of system (<a href="https://static-preview.hindawi.com/articles/jam/volume-2012/534276/figures/#EEq1.1">1.1</a>): <svg height="10.95" id="M335" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
</text>
</g>
</g>
</svg> = 0.21, <svg height="9.875" id="M336" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑝</tspan>
</text>
</g>
</g>
</svg> = 0.8, <svg height="11.1" id="M337" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 62.674999 11.1" width="62.674999" 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">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">0</tspan>
<tspan style="font-size: 12.50px; " x="37.534004" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="43.785507" y="0">5</tspan>
</text>
</g>
</g>
</svg>; (a) <svg height="13.55" id="M338" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 34.487499 13.55" width="34.487499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
<tspan style="font-size: 12.50px; " x="9.1897049" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.230095" y="0">3</tspan>
</text>
</g>
</g>
</svg>, (b) <svg height="13.675" id="M339" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 34.487499 13.675" width="34.487499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.675)">
<g transform="translate(72,-61.06)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
<tspan style="font-size: 12.50px; " x="9.1897049" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.230095" y="0">6</tspan>
</text>
</g>
</g>
</svg>, (c) <svg height="13.55" id="M340" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 42.299999 13.55" width="42.299999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
<tspan style="font-size: 12.50px; " x="9.1897049" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.230095" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="27.481594" y="0">0</tspan>
</text>
</g>
</g>
</svg>, (d) <svg height="13.7375" id="M341" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 54.025002 13.7375" width="54.025002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.7375)">
<g transform="translate(72,-61.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
<tspan style="font-size: 12.50px; " x="9.1897049" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.230095" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="27.481594" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="33.733093" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="36.858845" y="0">5</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Applied Mathematics

fig4

Figure 4

Figure 4: Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control 