Parameters

Like InitialConditions, the Parameters field of scotch model JSON files is a dictionary. Each key is the name of a parameter, as a string. Each value is a string expression for the value of that parameter.

"Parameters" : {
    "alpha" : "1/10",
    "beta" : "1 + sin(2 * pi * time)"
}

Values are required to be strings because parameter values are parsed into expressions that can be evaluated as lambdas. This allows a number of functions to be used :

• sin, sinh, arcsin, arcsinh
• cos, cosh, arccos, arccosh
• tan, tanh, arctan, arctanh
• exp, expm1 ( exp(x) - 1 )
• log, log10, log2, log1p ( log(1+x) )
• ceil, floor, abs
• sinc
• square, sqrt
• sign ( returns +1 or -1 )
• time

A number of reserved keywords also allow access to constants and to the explicit value of time :

• pi
• time ( allows time-dependent parameter rates to be used )

As an example, sin(2 * pi * sqrt(F) * time) is a legal part of a parameter value, if you have declared F as a state variable; this particular example allows parameters to vary sinusoidally in time. The time keyword is replaced by the numerical value of time during simulation. Parameters can therefore be state-dependent and time-dependent; they cannot, however, be written in terms of other parameters.

All numerical values are cast as floats, so expressions like 1/10 will be evaluated as 0.1.

Allowed operators are :

• +
• -
• *
• /
• **
• (, )

Currently, custom functions that cannot be written with this syntax will not evaluate.