diff --git a/docs/src/catalyst_applications/simulation_introduction.md b/docs/src/catalyst_applications/simulation_introduction.md index 8bcc45dc21..f4da9f3cff 100644 --- a/docs/src/catalyst_applications/simulation_introduction.md +++ b/docs/src/catalyst_applications/simulation_introduction.md @@ -1,7 +1,7 @@ # [Model Simulation Introduction](@id simulation_intro) Catalyst's core functionality is the creation of chemical reaction network (CRN) models that can be simulated using ODE, SDE, and jump simulations. How such simulations are carried out has already been described in [Catalyst's introduction](@ref introduction_to_catalyst). This page provides a deeper introduction, giving some additional background and introducing various simulation-related options. -Here we will focus on the basics, with other sections of the simulation documentation describing various specialised features, or giving advice on performance. Anyone who plans on using Catalyst's simulation function extensively is recommended to also read the documentation on [solution plotting](@ref ref), and on how to [interact with simulation problems, integrators, and solutions]. Anyone with an application for which performance is critical should consider reading the corresponding page on performance advice for [ODEs](@ref ref), [SDEs](@ref ref), or [jump simulations](@ref ref). +Here we will focus on the basics, with other sections of the simulation documentation describing various specialised features, or giving advice on performance. Anyone who plans on using Catalyst's simulation function extensively is recommended to also read the documentation on [solution plotting](@ref ref), and on how to [interact with simulation problems, integrators, and solutions](@ref ref). Anyone with an application for which performance is critical should consider reading the corresponding page on performance advice for [ODEs](@ref ref), [SDEs](@ref ref), or [jump simulations](@ref ref). ### [Background to CRN simulations](@id simulation_intro_theory) This section provides some brief theory on CRN simulations. For details of how to carry out these simulations in actual code, please skip to the following sections. @@ -10,7 +10,7 @@ CRNs are defined by a set of *species* (with the quantities of these determining In practice, these jump simulations are computationally expensive. In many cases, copy-numbers are so large that they can be approximated as *continuous concentrations*, and the time-development of the system as a *deterministic process*. This creates an ordinary differential equation (ODE), and is the chemical reaction network form most people are most familiar with. The rule for how ODEs are generated from CRNs is called the [*reaction rate equation*](https://en.wikipedia.org/wiki/Rate_equation) (RRE). -Here, the RRE enables fast (approximate) simulation of deterministic CRNs, while *stochastic chemical kinetics* enables exact, stochastic, simulated of the true process. An intermediary approach is to use the [*chemical Langevin equation*](https://pubs.aip.org/aip/jcp/article/113/1/297/184125/The-chemical-Langevin-equation) (CLE) to formulate a stochastic differential equation (SDE). This approximates the system's state as continuous concentrations, but *does not* assume that its time development is deterministic. Generally, the CLE is used when copy-numbers are large enough that the continuous approximation holds, but not so large that the system's behaviour is deterministic. Generally, the advantage of SDE simulations (compared to jump ones) is that they are faster. Also, since the system state is continuous, interpretation of e.g. stability and steady state results from the deterministic (also continuous) domain is easier for SDEs (however one should still be careful with these). +Here, the RRE enables fast, approximate, and deterministic simulations of CRNs, while *stochastic chemical kinetics* enables exact, stochastic, simulations of the true process. An intermediary approach is to use the [*chemical Langevin equation*](https://pubs.aip.org/aip/jcp/article/113/1/297/184125/The-chemical-Langevin-equation) (CLE) to formulate a stochastic differential equation (SDE). This approximates the system's state as continuous concentrations, but *does not* assume that its time development is deterministic. Generally, the CLE is used when copy-numbers are large enough that the continuous approximation holds, but not so large that the system's behaviour is deterministic. Generally, the advantage of SDE simulations (compared to jump ones) is that they are faster. Also, since the system state is continuous, interpretation of e.g. stability and steady state results from the deterministic (also continuous) domain is easier for SDEs (however one *should* be careful when making such interpretations). The different approaches are summed up in the following table: ```@raw html