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doc tweaks for v14 #977

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46 changes: 23 additions & 23 deletions README.md
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Expand Up @@ -43,7 +43,7 @@ documentation](https://docs.sciml.ai/Catalyst/stable/). The [in-development
documentation](https://docs.sciml.ai/Catalyst/dev/) describes unreleased features in
the current master branch.

An overview of the package, its features, and comparative benchmarking (as of version 13) can also
An overview of the package, its features, and comparative benchmarking (as of version 13) can also
be found in its corresponding research paper, [Catalyst: Fast and flexible modeling of reaction networks](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011530).

## Features
Expand Down Expand Up @@ -71,7 +71,7 @@ be found in its corresponding research paper, [Catalyst: Fast and flexible model
- [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) (reusing the Graphviz interface created in [Catlab.jl](https://algebraicjulia.github.io/Catlab.jl/stable/)).
- Model steady states can be computed through homotopy continuation using [HomotopyContinuation.jl](https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl) (which can find *all* steady states of systems with multiple ones), by forward ODE simulations using [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).
- [BifurcationKit.jl](https://github.com/bifurcationkit/BifurcationKit.jl) can be used to [compute bifurcation diagrams](https://docs.sciml.ai/Catalyst/stable/steady_state_functionality/bifurcation_diagrams/) of model steady states (including finding periodic orbits).
- [DynamicalSystems.jl](https://github.com/JuliaDynamics/DynamicalSystems.jl) can be used to compute 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).
- [DynamicalSystems.jl](https://github.com/JuliaDynamics/DynamicalSystems.jl) can be used to compute model [basins of attraction](@ref dynamical_systems_basins_of_attraction), [Lyapunov spectrums](@ref dynamical_systems_lyapunov_exponents), and other dynamical system properties.
- [StructuralIdentifiability.jl](https://github.com/SciML/StructuralIdentifiability.jl) can be used to [perform structural identifiability analysis](https://docs.sciml.ai/Catalyst/stable/inverse_problems/structural_identifiability/).
- [Optimization.jl](https://github.com/SciML/Optimization.jl), [DiffEqParamEstim.jl](https://github.com/SciML/DiffEqParamEstim.jl), 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/).
- [GlobalSensitivity.jl](https://github.com/SciML/GlobalSensitivity.jl) can be used to perform [global sensitivity analysis](https://docs.sciml.ai/Catalyst/stable/inverse_problems/global_sensitivity_analysis/) of model behaviors.
Expand All @@ -88,7 +88,7 @@ be found in its corresponding research paper, [Catalyst: Fast and flexible model
## Illustrative example

#### Deterministic ODE simulation of Michaelis-Menten enzyme kinetics
Here we show a simple example where a model is created using the Catalyst DSL, and then simulated as
Here we show a simple example where a model is created using the Catalyst DSL, and then simulated as
an ordinary differential equation.

```julia
Expand Down Expand Up @@ -129,14 +129,15 @@ plot(jump_sol; lw = 2)
![Jump simulation](docs/src/assets/readme_jump_plot.svg)


## Elaborate example
In the above example, we used basic Catalyst-based workflows to simulate a simple model. Here we
instead show how various Catalyst features can compose to create a much more advanced model. Our
model describes how the volume of a cell ($V$) is affected by a growth factor ($G$). The growth
factor only promotes growth while in its phosphorylated form ($Gᴾ$). The phosphorylation of $G$
($G \to Gᴾ$) is promoted by sunlight (modeled as the cyclic sinusoid $kₐ (sin(t) + 1)$), which
phosphorylates the growth factor (producing $Gᴾ$). When the cell reaches a critical volume ($Vₘ$)
it undergoes cell division. First, we declare our model:
## More elaborate example
In the above example, we used basic Catalyst workflows to simulate a simple
model. Here we instead show how various Catalyst features can compose to create
a much more advanced model. Our model describes how the volume of a cell ($V$)
is affected by a growth factor ($G$). The growth factor only promotes growth
while in its phosphorylated form ($G^P$). The phosphorylation of $G$ ($G \to G^P$)
is promoted by sunlight (modeled as the cyclic sinusoid $k_a (\sin(t) + 1)$),
which phosphorylates the growth factor (producing $G^P$). When the cell reaches a
critical volume ($V_m$) it undergoes cell division. First, we declare our model:
```julia
using Catalyst
cell_model = @reaction_network begin
Expand All @@ -151,22 +152,22 @@ cell_model = @reaction_network begin
kᵢ/V, Gᴾ --> G
end
```
We now study the system as a Chemical Langevin Dynamics SDE model, which can be generated as follows
We now study the system as a Chemical Langevin Dynamics SDE model, which can be generated as follows
```julia
u0 = [:V => 25.0, :G => 50.0, :Gᴾ => 0.0]
tspan = (0.0, 20.0)
ps = [:Vₘ => 50.0, :g => 0.3, :kₚ => 100.0, :kᵢ => 60.0]
sprob = SDEProblem(cell_model, u0, tspan, ps)
```
This produces the following equations:
This problem encodes the following stochastic differential equation model:
```math
\begin{align*}
dG(t) &= - \left( \frac{kₚ*(sin(t)+1)}{V(t)} G(t) + \frac{kᵢ}{V(t)} Gᴾ(t) \right) dt - \sqrt{\frac{kₚ*(sin(t)+1)}{V(t)} G(t)} dW_1(t) + \sqrt{\frac{kᵢ}{V(t)} Gᴾ(t)} dW_2(t) \\
dGᴾ(t) &= \left( \frac{kₚ*(sin(t)+1)}{V(t)} G(t) - \frac{kᵢ}{V(t)} Gᴾ(t) \right) dt + \sqrt{\frac{kₚ*(sin(t)+1)}{V(t)} G(t)} dW_1(t) - \sqrt{\frac{kᵢ}{V(t)} Gᴾ(t)} dW_2(t) \\
dV(t) &= \left(g \cdot Gᴾ(t)\right) dt
dG(t) &= - \left( \frac{k_p(\sin(t)+1)}{V(t)} G(t) + \frac{k_i}{V(t)} G^P(t) \right) dt - \sqrt{\frac{k_p (\sin(t)+1)}{V(t)} G(t)} \, dW_1(t) + \sqrt{\frac{k_i}{V(t)} G^P(t)} \, dW_2(t) \\
dG^P(t) &= \left( \frac{k_p(\sin(t)+1)}{V(t)} G(t) - \frac{k_i}{V(t)} G^P(t) \right) dt + \sqrt{\frac{k_p (\sin(t)+1)}{V(t)} G(t)} \, dW_1(t) - \sqrt{\frac{k_i}{V(t)} G^P(t)} \, dW_2(t) \\
dV(t) &= \left(g \, G^P(t)\right) dt
\end{align*}
```
where the $dW_1(t)$ and $dW_2(t)$ terms represent independent Brownian Motions, encoding the noise added by the Chemical Langevin Equation. Finally, we can simulate and plot the results.
where the $dW_1(t)$ and $dW_2(t)$ terms represent independent Brownian Motions, encoding the noise added by the Chemical Langevin Equation. Finally, we can simulate and plot the results.
```julia
using StochasticDiffEq, Plots
sol = solve(sprob, EM(); dt = 0.05)
Expand All @@ -181,15 +182,14 @@ Some features we used here:
- The model simulation was [plotted using Plots.jl](https://docs.sciml.ai/Catalyst/stable/model_simulation/simulation_plotting/).

## Getting help or getting involved
Catalyst developers are active on the [Julia Discourse](https://discourse.julialang.org/),
the [Julia Slack](https://julialang.slack.com) channels \#sciml-bridged and \#sciml-sysbio, and the
[Julia Zulip sciml-bridged channel](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged).
Catalyst developers are active on the [Julia Discourse](https://discourse.julialang.org/) and
the [Julia Slack](https://julialang.slack.com) channels \#sciml-bridged and \#sciml-sysbio.
For bugs or feature requests, [open an issue](https://github.com/SciML/Catalyst.jl/issues).

## Supporting and citing Catalyst.jl
The software in this ecosystem was developed as part of academic research. If you would like to help
support it, please star the repository as such metrics may help us secure funding in the future. If
you use Catalyst as part of your research, teaching, or other activities, we would be grateful if you
The software in this ecosystem was developed as part of academic research. If you would like to help
support it, please star the repository as such metrics may help us secure funding in the future. If
you use Catalyst as part of your research, teaching, or other activities, we would be grateful if you
could cite our work:
```
@article{CatalystPLOSCompBio2023,
Expand Down
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