Read the equation
The term −γC subtracts a contribution proportional to C, while I(t)[1+cos(φtFₙ)] injects a time-modulated input. The cosine multiplier lies between zero and two. For positive input it is nonnegative, but the net derivative can have either sign; nonnegative E is not automatically enforced by the differential equation.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| E | Energy-like state |
| γ | Consumption coefficient |
| C | Coupled state |
| I | External input function |
| F_n | Fibonacci integer |
| 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
\label{eq:dC}
\end{equation}
\begin{equation}
\frac{dE}{dt} = -\gamma C + I(t) \cdot \left(1 + \cos(\golden t \cdot \fib{n})\right)
\label{eq:dE}
\end{equation}
\begin{equation}
\frac{dL}{dt} = \delta(C - L) \cdot \frac{\fib{n}}{\fib{n} + \fib{n-1}}
\label{eq:dL}
\end{equation}Exact original notation
\frac{dE}{dt} = -\gamma C + I(t) \cdot \left(1 + \cos(\golden t \cdot \fib{n})\right)Related builds
Sources & provenance
\frac{dE}{dt} = -\gamma C + I(t) \cdot \left(1 + \cos(\golden t \cdot \fib{n})\right)
\frac{dE}{dt} = -\gamma C + I(t) \cdot \left(1 + \cos(\golden t \cdot \fib{n})\right)
\frac{dE}{dt} = -\gamma C + I(t) \cdot \left(1 + \cos(\golden t \cdot \fib{n})\right)
\frac{dE}{dt} = -\gamma C + I(t) \cdot \left(1 + \cos(\golden t \cdot \fib{n})\right)