Examining the Chaotic Behavior in Dynamical Systems by Means of the 0-1 Test

<table>(a) LCN versus Energy in 19th-order Hamiltonian, (b) Index <svg height="10.325" id="M129" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" 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">𝐾</tspan>
</text>
</g>
</g>
</svg> versus Energy in the 19th-order Hamiltonian. There is conformity of both curves, but the onset of strong chaos appears abruptly at <svg height="11.0375" id="M130" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 38.487499 11.0375" width="38.487499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0375)">
<g transform="translate(72,-63.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
<tspan style="font-size: 12.50px; " x="12.390473" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.430862" y="0">6</tspan>
</text>
</g>
</g>
</svg> and is better shown in (b).</table>

Journal of Applied Mathematics

fig6

Figure 6

Figure 6: Examining the Chaotic Behavior in Dynamical Systems by Means of the 0-1 Test 