Once we know all of the flows and how the system started, i.e. the initial values for the amounts in the different compartments, the behavior (dynamics) of the system is fully determined. What is more, it is easy to write the equations that give the dynamics. Suppose that Figure 3 is one compartment in such a system.
Figure 3
Here 
is the instantaneous rate of inflow
into compartment i from outside the system, for
example, an immigration rate in an epidemic model.
is the total flow rate from compartment j
into i and 
is the flow rate from i out of
the system. Knowing these instantaneous rates, one can
immediately write the dynamic equations for compartment
i by writing the mass balance equations for the rate
of change of the amount in i, i.e. 
.
The inflows are generally constant or functions of
time but the flow rates , 
and
can be functions of the compartment sizes,
, and possibly of time. All flows are
defined to be positive quantities so the signs take care
of the directions of flow. It turns out that under
fairly general conditions, one can write the flows
starting from a compartment in the form,
The 
are called transfer coefficients and may
also be functions of the compartment sizes. Using that,
equation (1) can be rwritten in the form,
That is the common form of the system equations and in the connectivity diagram it is the custom to label the transfers that start at compartments with their transfer coefficients rather than the total flows. If we write the set of equations for all of the compartments in a system, we have the system equations.