Read the equation
The derivative condition says C is momentarily not changing. A derivative of zero at one time is weaker than a constant equilibrium and much weaker than attraction to that equilibrium. For the manuscript’s time-dependent forcing, the condition must be checked across time before a constant steady state is asserted.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| C | Dynamical state |
| t | Time |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
\begin{proof}
The Fibonacci ratio $\fib{n}/\fib{n-1}$ converges to $\golden$ as $n \to \infty$. The modulation term $\sin(\golden t) \cdot \fib{n}/\fib{n-1}$ therefore oscillates with amplitude approaching $\golden$.
At equilibrium, $dC/dt = 0$, giving:
\begin{equation}
\alpha(E^* - C^*) + \beta \cdot L^* \cdot \sin(\golden t) \cdot \golden = 0
\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:Exact original notation
dC/dt = 0