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All-optical gain-clamped erbium-ytterbium (Er : Yb)-doped amplifier dynamic response is modeled and investigated. The complex Er:Yb rate equation system is reduced to a single equation. This simplification gives a more intuitive understanding of relevant physical mechanisms of Er:Yb doping. Experiments confirm theoretical assumptions. Results also allow us to describe dynamics in highly doped Er devices such as waveguide amplifiers.