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README.md

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[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://docs.sciml.ai/Catalyst/stable/)
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[![API Stable](https://img.shields.io/badge/API-stable-blue.svg)](https://docs.sciml.ai/Catalyst/stable/api/catalyst_api/)
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[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://docs.sciml.ai/Catalyst/dev/)
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[![API Dev](https://img.shields.io/badge/API-dev-blue.svg)](https://docs.sciml.ai/Catalyst/dev/api/catalyst_api/)
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[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://docs.sciml.ai/Catalyst/stable/)
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[![API Dev](https://img.shields.io/badge/API-dev-blue.svg)](https://docs.sciml.ai/Catalyst/stable/api/catalyst_api/)
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[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
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[![Build Status](https://github.com/SciML/Catalyst.jl/workflows/CI/badge.svg)](https://github.com/SciML/Catalyst.jl/actions?query=workflow%3ACI)
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[Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl), Catalyst enables
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large-scale simulations through auto-vectorization and parallelism. Symbolic
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`ReactionSystem`s can be used to generate ModelingToolkit-based models, allowing
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the easy simulation and parameter estimation of mass action ODE models, chemical
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the easy simulation and parameter estimation of mass action ODE models, Chemical
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Langevin SDE models, stochastic chemical kinetics jump process models, and more.
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Generated models can be used with solvers throughout the broader
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[SciML](https://sciml.ai) ecosystem, including higher-level SciML packages (e.g.
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The latest tutorials and information on using Catalyst are available in the [stable
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documentation](https://docs.sciml.ai/Catalyst/stable/). The [in-development
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documentation](https://docs.sciml.ai/Catalyst/dev/) describes unreleased features in
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documentation](https://docs.sciml.ai/Catalyst/stable/) describes unreleased features in
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the current master branch.
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An overview of the package, its features, and comparative benchmarking (as of version 13) can also
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## Features
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#### Features of Catalyst
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- [The Catalyst DSL](https://docs.sciml.ai/Catalyst/dev/model_creation/dsl_basics/) provides a simple and readable format for manually specifying reaction
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- [The Catalyst DSL](https://docs.sciml.ai/Catalyst/stable/model_creation/dsl_basics/) provides a simple and readable format for manually specifying reaction
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network models using chemical reaction notation.
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- Catalyst `ReactionSystem`s provides a symbolic representation of reaction networks,
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built on [ModelingToolkit.jl](https://docs.sciml.ai/ModelingToolkit/stable/) and
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multiple networks together.
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- Leveraging ModelingToolkit, generated models can be converted to symbolic reaction rate equation ODE models, symbolic Chemical Langevin Equation models, and symbolic stochastic chemical kinetics (jump process) models. These can be simulated using any
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[DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/)
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[ODE/SDE/jump solver](https://docs.sciml.ai/Catalyst/dev/model_simulation/simulation_introduction/), and can be used within `EnsembleProblem`s for carrying
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out [parallelized parameter sweeps and statistical sampling](https://docs.sciml.ai/Catalyst/dev/model_simulation/ensemble_simulations/). Plot recipes
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are available for [visualization of all solutions](https://docs.sciml.ai/Catalyst/dev/model_simulation/simulation_plotting/).
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- Non-integer (e.g. `Float64`) stoichiometric coefficients [are supported](https://docs.sciml.ai/Catalyst/dev/model_creation/dsl_basics/#dsl_description_stoichiometries_decimal) for generating
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ODE models, and symbolic expressions for stoichiometric coefficients [are supported](https://docs.sciml.ai/Catalyst/dev/model_creation/parametric_stoichiometry/) for
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[ODE/SDE/jump solver](https://docs.sciml.ai/Catalyst/stable/model_simulation/simulation_introduction/), and can be used within `EnsembleProblem`s for carrying
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out [parallelized parameter sweeps and statistical sampling](https://docs.sciml.ai/Catalyst/stable/model_simulation/ensemble_simulations/). Plot recipes
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are available for [visualization of all solutions](https://docs.sciml.ai/Catalyst/stable/model_simulation/simulation_plotting/).
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- Non-integer (e.g. `Float64`) stoichiometric coefficients [are supported](https://docs.sciml.ai/Catalyst/stable/model_creation/dsl_basics/#dsl_description_stoichiometries_decimal) for generating
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ODE models, and symbolic expressions for stoichiometric coefficients [are supported](https://docs.sciml.ai/Catalyst/stable/model_creation/parametric_stoichiometry/) for
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all system types.
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- A [network analysis suite](https://docs.sciml.ai/Catalyst/dev/model_creation/network_analysis/) permits the computation of linkage classes, deficiencies, reversibility, and other network properties.
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- [Conservation laws can be detected and utilized](https://docs.sciml.ai/Catalyst/dev/model_creation/network_analysis/#network_analysis_deficiency) to reduce system sizes, and to generate
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- A [network analysis suite](https://docs.sciml.ai/Catalyst/stable/model_creation/network_analysis/) permits the computation of linkage classes, deficiencies, reversibility, and other network properties.
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- [Conservation laws can be detected and utilized](https://docs.sciml.ai/Catalyst/stable/model_creation/network_analysis/#network_analysis_deficiency) to reduce system sizes, and to generate
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non-singular Jacobians (e.g. during conversion to ODEs, SDEs, and steady state equations).
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- Catalyst reaction network models can be [coupled with differential and algebraic equations](https://docs.sciml.ai/Catalyst/dev/model_creation/constraint_equations/)
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- Catalyst reaction network models can be [coupled with differential and algebraic equations](https://docs.sciml.ai/Catalyst/stable/model_creation/constraint_equations/)
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(which are then incorporated during conversion to ODEs, SDEs, and steady state equations).
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- Models can be [coupled with events](https://docs.sciml.ai/Catalyst/dev/model_creation/constraint_equations/#constraint_equations_events) that affect the system and its state during simulations.
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- Models can be [coupled with events](https://docs.sciml.ai/Catalyst/stable/model_creation/constraint_equations/#constraint_equations_events) that affect the system and its state during simulations.
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- By leveraging ModelingToolkit, users have a variety of options for generating
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optimized system representations to use in solvers. These include construction
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of [dense or sparse Jacobians](https://docs.sciml.ai/Catalyst/dev/model_simulation/ode_simulation_performance/#ode_simulation_performance_sparse_jacobian), [multithreading or parallelization of generated
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derivative functions](https://docs.sciml.ai/Catalyst/dev/model_simulation/ode_simulation_performance/#ode_simulation_performance_parallelisation), [automatic classification of reactions into optimized
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of [dense or sparse Jacobians](https://docs.sciml.ai/Catalyst/stable/model_simulation/ode_simulation_performance/#ode_simulation_performance_sparse_jacobian), [multithreading or parallelization of generated
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derivative functions](https://docs.sciml.ai/Catalyst/stable/model_simulation/ode_simulation_performance/#ode_simulation_performance_parallelisation), [automatic classification of reactions into optimized
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jump types for Gillespie type simulations](https://docs.sciml.ai/JumpProcesses/stable/jump_types/#jump_types), [automatic construction of
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dependency graphs for jump systems](https://docs.sciml.ai/JumpProcesses/stable/jump_types/#Jump-Aggregators-Requiring-Dependency-Graphs), and more.
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- [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl) symbolic
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expressions and Julia `Expr`s can be obtained for all rate laws and functions determining the
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deterministic and stochastic terms within resulting ODE, SDE or jump models.
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- [Steady states](https://docs.sciml.ai/Catalyst/dev/steady_state_functionality/homotopy_continuation/) (and their [stabilities](https://docs.sciml.ai/Catalyst/dev/steady_state_functionality/steady_state_stability_computation/)) can be computed for model ODE representations.
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- [Steady states](https://docs.sciml.ai/Catalyst/stable/steady_state_functionality/homotopy_continuation/) (and their [stabilities](https://docs.sciml.ai/Catalyst/stable/steady_state_functionality/steady_state_stability_computation/)) can be computed for model ODE representations.
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#### Features of Catalyst composing with other packages
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- [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl) Can be used to numerically solver generated reaction rate equation ODE models.
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- [StochasticDiffEq.jl](https://github.com/SciML/StochasticDiffEq.jl) can be used to numerically solve generated Chemical Langevin Equation SDE models.
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- [JumpProcesses.jl](https://github.com/SciML/JumpProcesses.jl) can be used to numerically sample generated Stochastic Chemical Kinetics Jump Process models.
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- Support for [parallelization of all simulations](https://docs.sciml.ai/Catalyst/dev/model_simulation/ode_simulation_performance/#ode_simulation_performance_parallelisation), including parallelization of
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[ODE simulations on GPUs](https://docs.sciml.ai/Catalyst/dev/model_simulation/ode_simulation_performance/#ode_simulation_performance_parallelisation_GPU) using
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- Support for [parallelization of all simulations](https://docs.sciml.ai/Catalyst/stable/model_simulation/ode_simulation_performance/#ode_simulation_performance_parallelisation), including parallelization of
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[ODE simulations on GPUs](https://docs.sciml.ai/Catalyst/stable/model_simulation/ode_simulation_performance/#ode_simulation_performance_parallelisation_GPU) using
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[DiffEqGPU.jl](https://github.com/SciML/DiffEqGPU.jl).
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- [Latexify](https://korsbo.github.io/Latexify.jl/stable/) can be used to [generate LaTeX
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expressions](https://docs.sciml.ai/Catalyst/dev/model_creation/model_visualisation/#visualisation_latex) corresponding to generated mathematical models or the
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expressions](https://docs.sciml.ai/Catalyst/stable/model_creation/model_visualisation/#visualisation_latex) corresponding to generated mathematical models or the
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underlying set of reactions.
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- [Graphviz](https://graphviz.org/) can be used to generate and [visualize reaction network graphs](https://docs.sciml.ai/Catalyst/dev/model_creation/model_visualisation/#visualisation_graphs)
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- [Graphviz](https://graphviz.org/) can be used to generate and [visualize reaction network graphs](https://docs.sciml.ai/Catalyst/stable/model_creation/model_visualisation/#visualisation_graphs)
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(reusing the Graphviz interface created in [Catlab.jl](https://algebraicjulia.github.io/Catlab.jl/stable/)).
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- Model steady states can be computed through homotopy continuation using [HomotopyContinuation.jl](https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl)
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(which can find *all* steady states of systems with multiple ones), by forward ODE simulations using
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[SteadyStateDiffEq.jl)](https://github.com/SciML/SteadyStateDiffEq.jl), or by numerically solving steady-state nonlinear equations using [NonlinearSolve.jl](https://github.com/SciML/NonlinearSolve.jl).
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- [BifurcationKit.jl](https://github.com/bifurcationkit/BifurcationKit.jl) can be used to [compute
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bifurcation diagrams](https://docs.sciml.ai/Catalyst/dev/steady_state_functionality/bifurcation_diagrams/) of models' steady states (including finding periodic orbits).
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bifurcation diagrams](https://docs.sciml.ai/Catalyst/stable/steady_state_functionality/bifurcation_diagrams/) of models' steady states (including finding periodic orbits).
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- [DynamicalSystems.jl](https://github.com/JuliaDynamics/DynamicalSystems.jl) can be used to compute
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model [basins of attraction](https://docs.sciml.ai/Catalyst/dev/steady_state_functionality/dynamical_systems/#dynamical_systems_basins_of_attraction) and [Lyapunov spectrums](https://docs.sciml.ai/Catalyst/dev/steady_state_functionality/dynamical_systems/#dynamical_systems_lyapunov_exponents).
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model [basins of attraction](https://docs.sciml.ai/Catalyst/stable/steady_state_functionality/dynamical_systems/#dynamical_systems_basins_of_attraction) and [Lyapunov spectrums](https://docs.sciml.ai/Catalyst/stable/steady_state_functionality/dynamical_systems/#dynamical_systems_lyapunov_exponents).
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- [StructuralIdentifiability.jl](https://github.com/SciML/StructuralIdentifiability.jl) can be used
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to [perform structural identifiability analysis](https://docs.sciml.ai/Catalyst/dev/inverse_problems/structural_identifiability/).
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to [perform structural identifiability analysis](https://docs.sciml.ai/Catalyst/stable/inverse_problems/structural_identifiability/).
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- [Optimization.jl](https://github.com/SciML/Optimization.jl), [DiffEqParamEstim.jl](https://github.com/SciML/DiffEqParamEstim.jl),
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and [PEtab.jl](https://github.com/sebapersson/PEtab.jl) can all be used to [fit model parameters to data](https://sebapersson.github.io/PEtab.jl/stable/Define_in_julia/).
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- [GlobalSensitivity.jl](https://github.com/SciML/GlobalSensitivity.jl) can be used to perform
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[global sensitivity analysis](https://docs.sciml.ai/Catalyst/dev/inverse_problems/global_sensitivity_analysis/) of model behaviors.
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[global sensitivity analysis](https://docs.sciml.ai/Catalyst/stable/inverse_problems/global_sensitivity_analysis/) of model behaviors.
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- [SciMLSensitivity.jl](https://github.com/SciML/SciMLSensitivity.jl) can be used to compute local sensitivities of functions containing forward model simulations.
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#### Features of packages built upon Catalyst
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- Catalyst [`ReactionSystem`](@ref)s can be [imported from SBML files](https://docs.sciml.ai/Catalyst/dev/model_creation/model_file_loading_and_export/#Loading-SBML-files-using-SBMLImporter.jl-and-SBMLToolkit.jl) via
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- Catalyst [`ReactionSystem`](@ref)s can be [imported from SBML files](https://docs.sciml.ai/Catalyst/stable/model_creation/model_file_loading_and_export/#Loading-SBML-files-using-SBMLImporter.jl-and-SBMLToolkit.jl) via
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[SBMLImporter.jl](https://github.com/SciML/SBMLImporter.jl) and [SBMLToolkit.jl](https://github.com/SciML/SBMLToolkit.jl),
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and [from BioNetGen .net files](https://docs.sciml.ai/Catalyst/dev/model_creation/model_file_loading_and_export/#file_loading_rni_net) and various stoichiometric matrix network representations
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and [from BioNetGen .net files](https://docs.sciml.ai/Catalyst/stable/model_creation/model_file_loading_and_export/#file_loading_rni_net) and various stoichiometric matrix network representations
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using [ReactionNetworkImporters.jl](https://github.com/SciML/ReactionNetworkImporters.jl).
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- [MomentClosure.jl](https://github.com/augustinas1/MomentClosure.jl) allows generation of symbolic
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ModelingToolkit `ODESystem`s that represent moment closure approximations to moments of the
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jump simulation
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```julia
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# Create and simulate a jump process (here using Gillespie's direct algorithm).
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# Note that integer (not decimal) initial conditions are used.
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using JumpProcesses
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u0_integers = [:S => 50, :E => 10, :SE => 0, :P => 0]
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dprob = DiscreteProblem(model, u0_integers, tspan, ps)
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![Elaborate SDE simulation](docs/src/assets/readme_elaborate_sde_plot.svg)
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Some features we used here:
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- The cell volume was [modeled as a differential equation, which was coupled to the reaction network model](https://docs.sciml.ai/Catalyst/dev/model_creation/constraint_equations/#constraint_equations_coupling_constraints).
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- The cell divisions were created by [incorporating events into the model](https://docs.sciml.ai/Catalyst/dev/model_creation/constraint_equations/#constraint_equations_events).
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- We designated a specific numeric [solver and corresponding solver options](https://docs.sciml.ai/Catalyst/dev/model_simulation/simulation_introduction/#simulation_intro_solver_options).
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- The model simulation was [plotted using Plots.jl](https://docs.sciml.ai/Catalyst/dev/model_simulation/simulation_plotting/).
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- The cell volume was [modeled as a differential equation, which was coupled to the reaction network model](https://docs.sciml.ai/Catalyst/stable/model_creation/constraint_equations/#constraint_equations_coupling_constraints).
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- The cell divisions were created by [incorporating events into the model](https://docs.sciml.ai/Catalyst/stable/model_creation/constraint_equations/#constraint_equations_events).
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- We designated a specific numeric [solver and corresponding solver options](https://docs.sciml.ai/Catalyst/stable/model_simulation/simulation_introduction/#simulation_intro_solver_options).
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- The model simulation was [plotted using Plots.jl](https://docs.sciml.ai/Catalyst/stable/model_simulation/simulation_plotting/).
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## Getting help or getting involved
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Catalyst developers are active on the [Julia Discourse](https://discourse.julialang.org/),

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