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Update docs/src/model_creation/functional_parameters.md
Co-authored-by: Sam Isaacson <[email protected]>
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docs/src/model_creation/functional_parameters.md

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# [Inputs and time-dependent (or functional) parameters](@id time_dependent_parameters)
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Catalyst supports the usage of "functional parameters". In practice these are not parameters, but a way to inject custom functions into models. This can be used when rates depend on real data, or to represent complicated functions ( which uses e.g. `for` loops or random number generation). Here, the function's values are declared as a data interpolation, which is then used as the functional parameter's value in the simulation. On this page, we first show how to create time-dependent functional parameters, and then give an example where the functional parameter depends on a species value.
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Catalyst supports the usage of "functional parameters". In practice these are parameters that are given by time-dependent functions, representing a way to inject custom functions into models. They can be used when rates depend on real data, or to represent complicated functions (which use e.g. `for` loops or random number generation). Here, the function's values are declared as a data interpolation, which is then used as the functional parameter's value in the simulation. On this page, we first show how to create time-dependent functional parameters, and then give an example where the functional parameter depends on a species value.
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## [Basic example](@id functional_parameters_basic_example)
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Let us first consider an easy, quick-start example. We will consider a simple [birth-death model](@ref basic_CRN_library_bd), but where the birth rate is determined by an input parameter (for which the value depends on time). First, we [define the input parameter programmatically](@ref programmatic_CRN_construction), and its values across all time points using the [DataInterpolations.jl](https://github.com/SciML/DataInterpolations.jl) package. In this example we will use the input function $pIn(t) = (2 + t)/(1 + t)$.

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