Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="595360.fig.002a" src="https://static.hindawi.com/articles/jam/volume-2012/595360/figures/595360.fig.002a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>The synchrony state <svg height="14.9" id="M168" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 95.449997 14.9" width="95.449997" xmlns="http://www.w3.org/2000/svg">
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<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
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<text transform="matrix(1,0,0,-1,-65.07,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑖</tspan>
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<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
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<tspan style="font-size: 12.50px; " x="13.890833" y="0">≤</tspan>
<tspan style="font-size: 12.50px; " x="25.918718" y="0">𝑖</tspan>
<tspan style="font-size: 12.50px; " x="33.282986" y="0">≤</tspan>
<tspan style="font-size: 12.50px; " x="45.323376" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="51.574875" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="57.826374" y="0">)</tspan>
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</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="595360.fig.002b" src="https://static.hindawi.com/articles/jam/volume-2012/595360/figures/595360.fig.002b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>The synchrony states <svg height="16.637501" id="M169" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 97.324997 16.637501" width="97.324997" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
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<tspan style="font-size: 12.50px; " x="13.87833" y="0">≤</tspan>
<tspan style="font-size: 12.50px; " x="25.918718" y="0">𝑗</tspan>
<tspan style="font-size: 12.50px; " x="34.258221" y="0">≤</tspan>
<tspan style="font-size: 12.50px; " x="46.286106" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="52.537605" y="0">0</tspan>
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<table>Cluster synchronization of the linearly coupled network (<a href="https://static.hindawi.com/articles/jam/volume-2012/595360/figures/#EEq3">3.6</a>) with 50 lorenz oscillators in the <svg height="7.1624999" id="M166" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" 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">𝑥</tspan>
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</svg>-cluster and 30 hyperchaotic Lü oscillators in the <svg height="9.8625002" id="M167" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.8625)">
<g transform="translate(72,-64.11)">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑦</tspan>
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</svg>-cluster.</table>

Journal of Applied Mathematics

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Figure 2

Figure 2: Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators 