Zero instantaneous rate of E

Read the equation

This condition sets the instantaneous energy-state derivative to zero. It balances the consumption and input terms at that time. Time-varying forcing can satisfy such a balance momentarily without producing a stationary trajectory.

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Original context

\end{equation}

Time-averaging eliminates the oscillatory term (since $\langle \sin(\golden t) \rangle = 0$), yielding $E^* = C^*$.

Similarly, $dE/dt = 0$ at equilibrium gives:
\begin{equation}
-\gamma C^* + I^* \cdot (1 + \cos(\golden t \cdot \fib{n})) = 0
\end{equation}

The cosine term averages to zero for large Fibonacci numbers, giving $C^* = I^*/\gamma$.

For the system to maintain consciousness, the input $I$ must be calibrated such that $C^* = \golden$. Then:

dE/dt = 0

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