The name is absent

^where            svar state variable name

avar      auxiliary variable name

rvar      rate variable name

evar      exogenous variable name

pname   parameter name

f (p)       function of parameters or other parameters, already declared

in the model code list

#         numeric constant

dt time step for the equation integration; it is inserted only to
identify a state equation but, really, any character set differing by
‘+’ or ‘*’ is allowed.

exp any algebraic expression containing #, pname, evar, avar, and svar.
In the expression, all the Stata functions can be used. For example,
it is possible to use the random generator function uniform()

label a descriptor of the statement (optional)

10) Special functions: simula recognizes some special functions that, indicated in the rate equations, perform some specific
tasks. These can be indicated only in the rate equations: moreover, each rate equation allows only one function. The syntax
of the functions is

R rvar=fcn expp, arg, arg,...]

where fcn is one of the special functions, exp is an algebraic expression and arg are the arguments needed by the function
itself. The available functions are, right now:

IDL information delay function. The syntax is “R rvar=IDL Xxpp d dly] ”, where dly is the delay time. The effect on rvar is
rvar_t = exp(t — dly) if t > dly and rvar_t = 0 otherwise.

MDL material delay function; this function has the same effect of a further level inserted in the flux, but not available to the user.
The syntax is “R rvar=MDL Xxxp d dly] ”, where dly is the delay time. The effect on rvar is rvar_t = rvar_t + exp(t — dly)
if t > dly and rvar_t = 0 otherwise. dly is expressed in time units. It must be a parameter or an auxiliary variable
name (not a constant or expression).

SWTC switch to rate on/off. The syntax is “R rvαz=SWTC[xxp,cvαr,von,vo_jf]”; sets the rate to zero if a control variable
cvar is below a low threshold value von or reaches an upper threshold voff. The results are rvar = 0 if cvar < von ;
rvar = exp if cvar > von and cvar < voff; and rvar = 0 if cvar ≥ voff. SWTC can be used to perform the tasks:

Represent a state variable with a physical limit and with the inflow rate independent from the level: von is set to 0
and voff to the maximum level capacity; cvar is the level itself.

Represent a process starting and/or stopping at some defined times: the control variable is _time; von and voff are the
starting and ending times.

Give a pulse of material at a specific time only (von = voff).

Simulate processes conditionally associated to other variables.

11) Simulation set-up: Time step, time span and time of start are defined by the command and not in the program.

Example of model coding

The .dct file containing a Volterra example model (without delay):

dictionary ■(

* file "volmodi.det"

* example model for "simula" STATA command (4/11/91)

* This is a kind of a VOLTERRA model - without delay

* Ref. J. Maynard Smith, 1974. Models in ecology. Cambridge University Press.

str70 _model "Model statements"

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