## System Dynamics Modules

*First Order Linear Negative Feedback*

The first-order negative feedback module comprises a stock progressively depleted
at a fractional decay rate. At any time, the absolute
value of the decay is indicted by the content of
the stock. More correctly, the initial sate will be depleted
over time to become the current state—the extent of the
decay can be gauged by counting all that flows out
over the period of interest. Rate of change of state
is negative and numerically equal to the product of the
current state of the system and a constant.

A first-order negative
feedback has the effect (each time we calculate it) of
subtracting from *S* an amount (where the constant is a
*Fractional Decay Factor* ‘*d*’) which is less than the previous
time we calculated it. Consider a series of calculations at
times *t0*, * t1*, *t2* ... *tn*, with the initial
value of *S* being *S0* and a Fractional Decay Factor
*d* operating on the outflow.

The description of the module is
at

The module coded in Powersim *Studio* is
at .

A demonstration of half-life decay using this
module can be found at F06HalfLifeDecay-SimulatorDemo.sip.

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