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- Model steady states can be [computed through homotopy continuation](@ref 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](@ref steady_state_solving_simulation) using [SteadyStateDiffEq.jl)](https://github.com/SciML/SteadyStateDiffEq.jl), or by [numerically solving steady-state nonlinear equations](@ref steady_state_solving_nonlinear) 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 bifurcation diagrams](@ref bifurcation_diagrams) of model steady states (including finding periodic orbits).
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-[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.
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-[StructuralIdentifiability.jl](https://github.com/SciML/StructuralIdentifiability.jl) can be used to [perform structural identifiability analysis](@ref structural_identifiability).
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<!--- [StructuralIdentifiability.jl](https://github.com/SciML/StructuralIdentifiability.jl) can be used to perform structural identifiability analysis.-->
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-[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/).
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-[GlobalSensitivity.jl](https://github.com/SciML/GlobalSensitivity.jl) can be used to perform [global sensitivity analysis](@ref 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.
Here, a good exercise is to check the resulting parameter set and note that, while it creates a good fit to the data, it does not actually correspond to the original parameter set. [Identifiability](@ref structural_identifiability) is a concept that studies how to deal with this problem.
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Here, a good exercise is to check the resulting parameter set and note that, while it creates a good fit to the data, it does not actually correspond to the original parameter set. Identifiabilityis a concept that studies how to deal with this problem.<!--NTS: re-add ref when identifiablity works again-->
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Say that we instead would like to use the [Broyden–Fletcher–Goldfarb–Shannon](https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm) algorithm, as implemented by the [Optim.jl](https://github.com/JuliaNLSolvers/Optim.jl) package. In this case we would run:
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```@example diffeq_param_estim_1
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---
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## References
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[^1]: [Alejandro F. Villaverde, Dilan Pathirana, Fabian Fröhlich, Jan Hasenauer, Julio R. Banga, *A protocol for dynamic model calibration*, Briefings in Bioinformatics (2023).](https://academic.oup.com/bib/article/23/1/bbab387/6383562?login=false)
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[^1]: [Alejandro F. Villaverde, Dilan Pathirana, Fabian Fröhlich, Jan Hasenauer, Julio R. Banga, *A protocol for dynamic model calibration*, Briefings in Bioinformatics (2023).](https://academic.oup.com/bib/article/23/1/bbab387/6383562?login=false)
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