A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions

<table>Spatiotemporal chaos in the DCML (<a href="https://static.hindawi.com/articles/ddns/volume-2011/174376/figures/#EEq3.4">3.18</a>) without any control, with parameters <svg height="10.9125" id="M268" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 56.262501 10.9125" width="56.262501" 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">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="14.103384" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.143772" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="32.395271" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="38.646774" y="0">0</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M269" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 46.900002 10.9125" width="46.900002" 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">𝑎</tspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.031727" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.157476" y="0">8</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M270" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 54.212502 10.9125" width="54.212502" 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">𝜖</tspan>
<tspan style="font-size: 12.50px; " x="9.3397408" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.380131" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="27.63163" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="30.75738" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.008881" y="0">1</tspan>
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</svg>.</table>

Discrete Dynamics in Nature and Society

fig1

Figure 1

Figure 1: A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions 