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@@ -216,7 +216,6 @@ <h3>4D Coupled System Dynamics</h3>
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<p><strong>Exotic Instabilities:</strong> Expanding to 4 dimensions (position and velocity for both pendulums) unlocks exotic behaviors that are mathematically forbidden in the 2D system.</p>
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<li><strong>Neimark-Sacker Bifurcation:</strong> Set $\delta_1=1$, $\delta_2=2.5$, $c_1=0$, $c_2=0.5$, $k=1$, and slowly increase $\epsilon$. Because $\prod \lambda_i = e^{-(c_1+c_2)\pi}$, a complex conjugate pair can now cross the unit circle while the other pair shrinks. This creates quasi-periodic torus shapes in phase space!</li>
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<li><strong>Co-existing Instabilities:</strong> You can observe multiple distinct modes of instability simultaneously. For example, by using negative stiffnesses, both pendulums can undergo extreme real-axis resonances concurrently.</li>
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