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Copy file name to clipboardExpand all lines: docs/src/index.md
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-[Steady states](@ref homotopy_continuation) (and their [stabilities](@ref steady_state_stability)) can be computed for model ODE representations.
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#### [Features of Catalyst composing with other packages](@id doc_index_features_composed)
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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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-[OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl) Can be used to numerically solve 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](@ref ode_simulation_performance_parallelisation), including parallelization of [ODE simulations on GPUs](@ref ode_simulation_performance_parallelisation_GPU) using [DiffEqGPU.jl](https://github.com/SciML/DiffEqGPU.jl).
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Many Catalyst features require the installation of additional packages. E.g. for ODE-solving and simulation plotting
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```julia
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Pkg.add("OrdinaryDiffEq")
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Pkg.add("OrdinaryDiffEqDefault")
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Pkg.add("Plots")
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```
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is also needed.
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Copy file name to clipboardExpand all lines: docs/src/introduction_to_catalyst/catalyst_for_new_julia_users.md
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using Pkg
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Pkg.add("Catalyst")
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```
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Here, the Julia package manager package (`Pkg`) is by default installed on your computer when Julia is installed, and can be activated directly. Next, we also wish to install the `OrdinaryDiffEq` and `Plots`packages (for numeric simulation of models, and plotting, respectively).
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Here, the Julia package manager package (`Pkg`) is by default installed on your computer when Julia is installed, and can be activated directly. Next, we install an ODE solver from a sub-library of the larger `OrdinaryDiffEq`package, and install the `Plots`package for making graphs. We will import the recommended default solver from the `OrdinaryDiffEqDefault` sub-library. A full list of `OrdinaryDiffEq` solver sublibraries can be found on the sidebar of [this page](https://docs.sciml.ai/OrdinaryDiffEq/stable/).
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```julia
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Pkg.add("OrdinaryDiffEq")
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Pkg.add("OrdinaryDiffEqDefault")
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Pkg.add("Plots")
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```
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Once a package has been installed through the `Pkg.add` command, this command does not have to be repeated if we restart our Julia session. We can now import all three packages into our current session with:
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```@example ex2
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using Catalyst
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using OrdinaryDiffEq
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using OrdinaryDiffEqDefault
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using Plots
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```
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Here, if we restart Julia, these `using` commands *must be rerun*.
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---
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## References
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[^1]: [Torkel E. Loman, Yingbo Ma, Vasily Ilin, Shashi Gowda, Niklas Korsbo, Nikhil Yewale, Chris Rackauckas, Samuel A. Isaacson, *Catalyst: Fast and flexible modeling of reaction networks*, PLOS Computational Biology (2023).](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011530)
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[^2]: [Jeff Bezanson, Alan Edelman, Stefan Karpinski, Viral B. Shah, *Julia: A Fresh Approach to Numerical Computing*, SIAM Review (2017).](https://epubs.siam.org/doi/abs/10.1137/141000671)
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[^2]: [Jeff Bezanson, Alan Edelman, Stefan Karpinski, Viral B. Shah, *Julia: A Fresh Approach to Numerical Computing*, SIAM Review (2017).](https://epubs.siam.org/doi/abs/10.1137/141000671)
We next load the basic packages we'll need for our first example:
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```@example tut1
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using Catalyst, OrdinaryDiffEq, Plots, Latexify
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using Catalyst, OrdinaryDiffEqTsit5, Plots, Latexify
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```
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Let's start by using the Catalyst [`@reaction_network`](@ref) macro to specify a
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---
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## References
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1.[Torkel E. Loman, Yingbo Ma, Vasily Ilin, Shashi Gowda, Niklas Korsbo, Nikhil Yewale, Chris Rackauckas, Samuel A. Isaacson, *Catalyst: Fast and flexible modeling of reaction networks*, PLOS Computational Biology (2023).](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011530)
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1.[Torkel E. Loman, Yingbo Ma, Vasily Ilin, Shashi Gowda, Niklas Korsbo, Nikhil Yewale, Chris Rackauckas, Samuel A. Isaacson, *Catalyst: Fast and flexible modeling of reaction networks*, PLOS Computational Biology (2023).](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011530)
Copy file name to clipboardExpand all lines: docs/src/inverse_problems/behaviour_optimisation.md
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```
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To demonstrate this pulsing behaviour we will simulate the system for an example parameter set. We select an initial condition (`u0`) so the system begins in a steady state.
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```@example behaviour_optimization
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using OrdinaryDiffEq, Plots
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using OrdinaryDiffEqTsit5, Plots
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example_p = [:pX => 0.1, :pY => 1.0, :pZ => 1.0]
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tspan = (0.0, 50.0)
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example_u0 = [:X => 0.1, :Y => 0.1, :Z => 1.0]
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---
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## References
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[^1]: [Mykel J. Kochenderfer, Tim A. Wheeler *Algorithms for Optimization*, The MIT Press (2019).](https://algorithmsbook.com/optimization/files/optimization.pdf)
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[^2]: [Lea Goentoro, Oren Shoval, Marc W Kirschner, Uri Alon *The incoherent feedforward loop can provide fold-change detection in gene regulation*, Molecular Cell (2009).](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2896310/)
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[^2]: [Lea Goentoro, Oren Shoval, Marc W Kirschner, Uri Alon *The incoherent feedforward loop can provide fold-change detection in gene regulation*, Molecular Cell (2009).](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2896310/)
Copy file name to clipboardExpand all lines: docs/src/inverse_problems/global_sensitivity_analysis.md
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```
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We will study the peak number of infected cases's ($max(I(t))$) sensitivity to the system's three parameters. We create a function which simulates the system from a given initial condition and measures this property:
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---
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## References
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[^1]: [Saltelli, A et al. *Global Sensitivity Analysis. The Primer*, Wiley (2008).](http://www.andreasaltelli.eu/file/repository/A_Saltelli_Marco_Ratto_Terry_Andres_Francesca_Campolongo_Jessica_Cariboni_Debora_Gatelli_Michaela_Saisana_Stefano_Tarantola_Global_Sensitivity_Analysis_The_Primer_Wiley_Interscience_2008_.pdf)
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[^1]: [Saltelli, A et al. *Global Sensitivity Analysis. The Primer*, Wiley (2008).](http://www.andreasaltelli.eu/file/repository/A_Saltelli_Marco_Ratto_Terry_Andres_Francesca_Campolongo_Jessica_Cariboni_Debora_Gatelli_Michaela_Saisana_Stefano_Tarantola_Global_Sensitivity_Analysis_The_Primer_Wiley_Interscience_2008_.pdf)
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