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docs/src/assets/Project.toml

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@@ -35,7 +35,7 @@ DataFrames = "1"
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DiffEqParamEstim = "2.1"
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DifferentialEquations = "7.7"
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Distributions = "0.25"
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Documenter = "0.27"
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Documenter = "1.4.1"
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HomotopyContinuation = "2.6"
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Latexify = "0.15, 0.16"
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ModelingToolkit = "9.5"

docs/src/introduction_to_catalyst/catalyst_for_new_julia_users.md

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```
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Here, if we restart Julia, these commands *do need to be rerun.
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A more comprehensive (but still short) introduction to package management in Julia is provided at [the end of this documentation page](catalyst_for_new_julia_users_packages). It contains some useful information and is hence highly recommended reading. For a more detailed introduction to Julia package management, please read [the Pkg documentation](https://docs.julialang.org/en/v1/stdlib/Pkg/).
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A more comprehensive (but still short) introduction to package management in Julia is provided at [the end of this documentation page](@ref catalyst_for_new_julia_users_packages). It contains some useful information and is hence highly recommended reading. For a more detailed introduction to Julia package management, please read [the Pkg documentation](https://docs.julialang.org/en/v1/stdlib/Pkg/).
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## Simulating a basic Catalyst model
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Now that we have some basic familiarity with Julia, and have installed and imported the required packages, we will create and simulate a basic chemical reaction network model using Catalyst.

docs/src/model_creation/dsl_description.md

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```
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similarly, we can plot the values of $Xtot$ and $Ytot$ using
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```@example obs1
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using plots
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plot(sol; idxs=[:Xtot, :Ytot], label=["Total X" "Total Y"])
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```
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docs/src/model_simulation/TOBEREMOVED_advanced_simulations.md

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`5.0` to its amount. We can now simulate our system using the
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callback:
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```@example ex2
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sol = solve(oprob; callback = ps_cb)
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sol = solve(oprob, Tsit5(); callback = ps_cb)
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plot(sol)
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```
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oprob = ODEProblem(rn, u0, tspan, p)
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condition = [5.0]
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affect!(integrator) = integrator[:k] = 5.0
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affect!(integrator) = integrator.ps[:k] = 5.0
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ps_cb = PresetTimeCallback(condition, affect!)
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sol = solve(oprob; callback = ps_cb)
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sol = solve(oprob, Tsit5(); callback = ps_cb)
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plot(sol)
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```
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The result looks as expected. However, what happens if we attempt to run the
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simulation again?
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```@example ex2
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sol = solve(oprob; callback = ps_cb)
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sol = solve(oprob, Tsit5(); callback = ps_cb)
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plot(sol)
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```
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The plot looks different, even though we simulate the same problem. Furthermore,
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affect!(integrator) = integrator.ps[:k] = 5.0
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ps_cb = PresetTimeCallback(condition, affect!)
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sol = solve(deepcopy(oprob); callback = ps_cb)
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sol = solve(deepcopy(oprob), Tsit5(); callback = ps_cb)
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plot(sol)
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```
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where we parse a copy of our `ODEProblem` to the solver (using `deepcopy`). We can now run
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```@example ex2
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sol = solve(deepcopy(oprob); callback = ps_cb)
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sol = solve(deepcopy(oprob), Tsit5(); callback = ps_cb)
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plot(sol)
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```
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and get the expected result.
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ps_cb_1 = PresetTimeCallback([3.0, 7.0], integ -> integ[:X1] += 5.0)
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ps_cb_2 = PresetTimeCallback([5.0], integ -> integ[:k] = 5.0)
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sol = solve(deepcopy(oprob); callback=CallbackSet(ps_cb_1, ps_cb_2))
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sol = solve(deepcopy(oprob), Tsit5(); callback=CallbackSet(ps_cb_1, ps_cb_2))
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plot(sol)
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```
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u0_4 = [:X => 10.0, :Y => 10.0]
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tspan = (0.0, 10.0)
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p_4 = [p => 10.0, d => 1.]
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p_4 = [:p => 10.0, :d => 1.]
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sprob_4 = SDEProblem(rn_4, u0_4, tspan, p_4)
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sol_4 = solve(sprob_4, ImplicitEM())

docs/src/model_simulation/simulation_structure_interfacing.md

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Catalyst is built on an *intermediary representation* implemented by (ModelingToolkit.jl)[https://github.com/SciML/ModelingToolkit.jl]. ModelingToolkit is a modelling framework where one first declares a set of symbolic variables and parameters using e.g.
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```@example ex2
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using Catalyst # hide
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using ModelingToolkit
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t = default_t()
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@parameters σ ρ β

docs/src/steady_state_functionality/nonlinear_solve.md

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## [Systems with conservation laws](@id nonlinear_solve_conservation_laws)
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As described in the section on homotopy continuation, when finding the steady states of systems with conservation laws, [additional considerations have to be taken](homotopy_continuation_conservation_laws). E.g. consider the following two-state system:
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As described in the section on homotopy continuation, when finding the steady states of systems with conservation laws, [additional considerations have to be taken](@ref homotopy_continuation_conservation_laws). E.g. consider the following two-state system:
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```@example nonlinear_solve2
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using Catalyst, NonlinearSolve # hide
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two_state_model = @reaction_network begin

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