BifurcationProblem drops observed variables from ODESystem

Describe the bug 🐞

Using observed variables in the RHS of an ODESystem leads to errors when computing bifurcation diagrams.

Expected behavior

A bifurcation diagram should be plotted, instead an error is thrown because the observed variable is not defined.

Minimal Reproducible Example 👇

using ModelingToolkit
using BifurcationKit
using ModelingToolkit: t_nounits as t, D_nounits as D

@mtkmodel FOL begin
    @parameters begin
        τ # parameters
    end
    @variables begin
        x(t) # dependent variables
        RHS(t)
    end
    @equations begin
        RHS ~ (1 - x) / τ
        D(x) ~ RHS
    end
end

@mtkbuild fol = FOL()

par = [fol.τ => 1.]
u0 = [fol.x => 1.]
prob = ODEProblem(fol, u0, (0.0, 1.), par)

bif_par = fol.τ

bp = BifurcationProblem(fol, u0, par, bif_par)

opts_br = ContinuationPar(p_min = 0.5,
    p_max = 2.)

bf = bifurcationdiagram(bp, PALC(), 2, opts_br)

Error & Stacktrace ⚠️

ERROR: UndefVarError: `RHS` not defined
Stacktrace:
  [1] macro expansion
    @ C:\Users\pmzmo\.julia\packages\SymbolicUtils\EGhOJ\src\code.jl:468 [inlined]
  [2] macro expansion
    @ C:\Users\pmzmo\.julia\packages\RuntimeGeneratedFunctions\M9ZX8\src\RuntimeGeneratedFunctions.jl:163 [inlined]
  [3] macro expansion
    @ .\none:0 [inlined]
  [4] generated_callfunc
    @ .\none:0 [inlined]
  [5] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Vector{…}, ::Vector{…})
    @ RuntimeGeneratedFunctions C:\Users\pmzmo\.julia\packages\RuntimeGeneratedFunctions\M9ZX8\src\RuntimeGeneratedFunctions.jl:150
  [6] f
    @ C:\Users\pmzmo\.julia\packages\ModelingToolkit\U2JaS\src\systems\nonlinear\nonlinearsystem.jl:289 [inlined]
  [7] residual
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Problems.jl:69 [inlined]
  [8] residual
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Problems.jl:269 [inlined]
  [9] _newton(prob::BifurcationProblem{…}, x0::Vector{…}, p0::Vector{…}, options::NewtonPar{…}; normN::typeof(LinearAlgebra.norm), callback::typeof(BifurcationKit.cb_default), kwargs::@Kwargs{…})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Newton.jl:75
 [10] _newton
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Newton.jl:67 [inlined]
 [11] newton
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Newton.jl:146 [inlined]
 [12] iterate(it::ContIterable{…}; _verbosity::UInt8)
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:357
 [13] iterate
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:338 [inlined]
 [14] continuation(it::ContIterable{…})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:570
 [15] continuation(prob::BifurcationProblem{…}, alg::PALC{…}, contparams::ContinuationPar{…}; linear_algo::Nothing, bothside::Bool, kwargs::@Kwargs{})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:648
 [16] continuation
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:618 [inlined]
 [17] bifurcationdiagram(prob::BifurcationProblem{…}, alg::PALC{…}, level::Int64, options::BifurcationKit.var"#717#718"{…}; linear_algo::Nothing, kwargs::@Kwargs{})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:108
 [18] bifurcationdiagram
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:101 [inlined]
 [19] #bifurcationdiagram#716
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:120 [inlined]
 [20] bifurcationdiagram(prob::BifurcationProblem{…}, alg::PALC{…}, level::Int64, options::ContinuationPar{…})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:115
 [21] top-level scope
    @ c:\Users\pmzmo\OneDrive - The University of Nottingham\Documents\Julia\ContinuationForOptimisation\mre.jl:32
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

Output of using Pkg; Pkg.status()

Status `C:\Users\pmzmo\.julia\environments\v1.10\Project.toml`
  [0f109fa4] BifurcationKit v0.3.6
  [03cb29e0] CellMLToolkit v2.12.0
  [187b0558] ConstructionBase v1.5.5
  [0c46a032] DifferentialEquations v7.13.0
  [61744808] DynamicalSystems v3.3.17
  [961ee093] ModelingToolkit v9.24.0
  [d96e819e] Parameters v0.12.3
  [91a5bcdd] Plots v1.40.5
  [295af30f] Revise v3.5.15

Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `C:\Users\pmzmo\.julia\environments\v1.10\Manifest.toml`
  [47edcb42] ADTypes v1.6.1
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.36
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
⌅ [7d9fca2a] Arpack v0.5.3
  [4fba245c] ArrayInterface v7.12.0
  [4c555306] ArrayLayouts v1.10.2
  [f3fd9213] Attractors v1.18.5
  [13072b0f] AxisAlgorithms v1.1.0
  [aae01518] BandedMatrices v1.7.2
  [0f109fa4] BifurcationKit v0.3.6
  [e2ed5e7c] Bijections v0.1.7
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [a134a8b2] BlackBoxOptim v0.6.3
  [8e7c35d0] BlockArrays v1.1.0
  [764a87c0] BoundaryValueDiffEq v5.9.0
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [a9c8d775] CPUTime v1.0.0
  [96374032] CRlibm v1.0.1
  [00ebfdb7] CSTParser v3.4.3
  [49dc2e85] Calculus v0.5.1
  [03cb29e0] CellMLToolkit v2.12.0
  [d360d2e6] ChainRulesCore v1.24.0
  [608a59af] ChaosTools v3.1.2
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [aaaa29a8] Clustering v0.15.7
  [da1fd8a2] CodeTracking v1.3.5
  [944b1d66] CodecZlib v0.7.5
  [35d6a980] ColorSchemes v3.25.0
  [3da002f7] ColorTypes v0.11.5
  [c3611d14] ColorVectorSpace v0.10.0
  [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.15.0
  [ab4b797d] ComplexityMeasures v3.6.4
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
  [187b0558] ConstructionBase v1.5.5
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [717857b8] DSP v0.7.9
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [bcd4f6db] DelayDiffEq v5.47.3
  [5732040d] DelayEmbeddings v2.7.4
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.151.5
  [459566f4] DiffEqCallbacks v3.6.2
  [77a26b50] DiffEqNoiseProcess v5.22.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.13.0
  [a0c0ee7d] DifferentiationInterface v0.5.9
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.109
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [fa6b7ba4] DualNumbers v0.6.8
⌅ [7c1d4256] DynamicPolynomials v0.5.7
⌅ [06fc5a27] DynamicQuantities v0.13.2
  [61744808] DynamicalSystems v3.3.17
  [6e36e845] DynamicalSystemsBase v3.8.3
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.7.7
  [90fa49ef] ErrorfreeArithmetic v0.5.2
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
  [8f5d6c58] EzXML v1.2.0
  [c87230d0] FFMPEG v0.4.1
  [7a1cc6ca] FFTW v1.8.0
  [9d29842c] FastAlmostBandedMatrices v0.1.3
  [7034ab61] FastBroadcast v0.3.4
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.0.2
  [29a986be] FastLapackInterface v2.0.4
  [fa42c844] FastRounding v0.3.1
  [1a297f60] FillArrays v1.11.0
  [64ca27bc] FindFirstFunctions v1.2.0
  [6a86dc24] FiniteDiff v2.23.1
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
  [4665ce21] FractalDimensions v1.8.1
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.11
  [46192b85] GPUArraysCore v0.1.6
  [28b8d3ca] GR v0.73.6
  [c145ed77] GenericSchur v0.5.4
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.11.2
  [42e2da0e] Grisu v1.0.2
  [cd3eb016] HTTP v1.10.8
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.23
  [09f84164] HypothesisTests v0.11.0
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [a98d9a8b] Interpolations v0.15.1
⌅ [d1acc4aa] IntervalArithmetic v0.20.9
  [d2bf35a9] IntervalRootFinding v0.5.11
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.15
  [92d709cd] IrrationalConstants v0.2.2
  [c8e1da08] IterTools v1.10.0
  [42fd0dbc] IterativeSolvers v0.9.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.7
  [692b3bcd] JLLWrappers v1.5.0
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.57
  [aa1ae85d] JuliaInterpreter v0.9.32
  [ccbc3e58] JumpProcesses v9.11.1
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.6
  [0b1a1467] KrylovKit v0.8.1
  [b964fa9f] LaTeXStrings v1.3.1
  [2ee39098] LabelledArrays v1.16.0
  [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.4
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.1.9
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.2.0
  [7a12625a] LinearMaps v3.11.3
  [7ed4a6bd] LinearSolve v2.30.2
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.0.3
  [fc60dff9] LombScargle v1.0.3
  [bdcacae8] LoopVectorization v0.12.171
  [6f1432cf] LoweredCodeUtils v2.4.8
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [299715c1] MarchingCubes v0.1.9
  [abcecc63] MathML v0.1.15
  [a3b82374] MatrixFactorizations v3.0.0
  [bb5d69b7] MaybeInplace v0.1.3
  [739be429] MbedTLS v1.1.9
  [eff96d63] Measurements v2.11.0
  [442fdcdd] Measures v0.3.2
  [c03570c3] Memoize v0.4.4
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.24.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.6
  [d8a4904e] MutableArithmetics v1.4.5
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.2
  [b8a86587] NearestNeighbors v0.4.18
  [645ca80c] Neighborhood v0.2.4
  [8913a72c] NonlinearSolve v3.13.1
  [6fe1bfb0] OffsetArrays v1.14.1
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.86.0
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.2.0
  [995b91a9] PlotUtils v1.4.1
  [91a5bcdd] Plots v1.40.5
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.15
  [1d0040c9] PolyesterWeave v0.2.2
⌅ [f27b6e38] Polynomials v3.2.13
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.22
  [aea7be01] PrecompileTools v1.2.1
  [31e2f376] PredefinedDynamicalSystems v1.2.0
  [21216c6a] Preferences v1.4.3
  [92933f4c] ProgressMeter v1.10.1
  [43287f4e] PtrArrays v1.2.0
  [1fd47b50] QuadGK v2.9.4
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.5.3
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [639c3291] RecurrenceAnalysis v2.0.8
  [731186ca] RecursiveArrayTools v3.26.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [295af30f] Revise v3.5.15
  [79098fc4] Rmath v0.7.1
  [f2b01f46] Roots v2.1.5
  [5eaf0fd0] RoundingEmulator v0.2.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.42.0
  [c0aeaf25] SciMLOperators v0.3.8
  [53ae85a6] SciMLStructures v1.4.1
  [6c6a2e73] Scratch v1.2.1
  [3cc68bcd] SetRounding v0.2.1
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.1.0
  [727e6d20] SimpleNonlinearSolve v1.10.1
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.19.0
  [0a514795] SparseMatrixColorings v0.3.5
  [e56a9233] Sparspak v0.3.9
  [d4ead438] SpatialIndexing v0.1.6
  [276daf66] SpecialFunctions v2.4.0
  [40b095a5] StateSpaceSets v1.4.6
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.5.1
  [90137ffa] StaticArrays v1.9.7
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.1
  [9672c7b4] SteadyStateDiffEq v2.2.0
  [789caeaf] StochasticDiffEq v6.66.0
  [7792a7ef] StrideArraysCore v0.5.7
  [09ab397b] StructArrays v0.6.18
  [c3572dad] Sundials v4.24.0
  [2efcf032] SymbolicIndexingInterface v0.3.26
  [19f23fe9] SymbolicLimits v0.2.1
  [d1185830] SymbolicUtils v2.1.2
  [0c5d862f] Symbolics v5.33.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.4.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [c804724b] TimeseriesSurrogates v2.7.1
  [0796e94c] Tokenize v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.0
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [b8865327] UnicodePlots v3.6.4
  [1986cc42] Unitful v1.20.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [41fe7b60] Unzip v0.2.0
  [409d34a3] VectorInterface v0.4.6
  [3d5dd08c] VectorizationBase v0.21.70
  [19fa3120] VertexSafeGraphs v0.2.0
  [29a6e085] Wavelets v0.10.0
  [efce3f68] WoodburyMatrices v1.0.0
⌅ [68821587] Arpack_jll v3.5.1+1
  [6e34b625] Bzip2_jll v1.0.8+1
  [4e9b3aee] CRlibm_jll v1.0.1+0
  [83423d85] Cairo_jll v1.18.0+2
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [f5851436] FFTW_jll v3.3.10+0
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+0
  [d2c73de3] GR_jll v0.73.6+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.80.2+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [1d5cc7b8] IntelOpenMP_jll v2024.2.0+0
  [aacddb02] JpegTurbo_jll v3.0.3+0
  [c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
  [1d63c593] LLVMOpenMP_jll v15.0.7+0
  [dd4b983a] LZO_jll v2.10.2+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.11+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.49.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.40.1+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.14+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.4.2+0
⌅ [fb77eaff] Sundials_jll v5.2.2+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.1+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.4.6+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.6+0
  [35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.43+1
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

Output of versioninfo()

Julia Version 1.10.4
Commit 48d4fd4843 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 4 × Intel(R) Core(TM) i3-8130U CPU @ 2.20GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

Additional context

When an ODESystem is used to construct a BifurcationProblem, only the equations, parameters and unknowns are included. If an observed variable, with its own equations, if used in the RHS of any of the ODEs, then it will be undefined in the resulting NonlinearSystem.

The following code provides a workaround by ensuring ALL observed variables and equations are included in the NonlinearSystem (and skipping the ODESystem conversion step). This also requires including initial guesses for the observed variables.

using ModelingToolkit
using BifurcationKit
using ModelingToolkit: t_nounits as t, D_nounits as D

@mtkmodel FOL begin
    @parameters begin
        τ # parameters
    end
    @variables begin
        x(t) # dependent variables
        RHS(t)
    end
    @equations begin
        RHS ~ (1 - x) / τ
        D(x) ~ RHS
    end
end

@mtkbuild fol = FOL()

par = [fol.τ => 1.]
u0 = [fol.x => 1.]
prob = ODEProblem(fol, u0, (0.0, 1.), par)

bif_par = fol.τ

# Define the NonlinearSystem to include observed variables
nsys = NonlinearSystem([[0 ~ eq.rhs for eq in equations(fol)]; [eq for eq in observed(fol)]],
    [unknowns(fol); [eq.lhs for eq in observed(fol)]],
    parameters(fol);
    name = nameof(fol))
# This means observed variables are now unknowns and so need initial guesses
u0 = [u0; [fol.RHS => (1 - 1.) / 1.]]

bp = BifurcationProblem(complete(nsys), u0, par, bif_par)

opts_br = ContinuationPar(p_min = 0.5,
    p_max = 2.)

bf = bifurcationdiagram(bp, PALC(), 2, opts_br)

Not sure if its best to have a system like this (where observed variables and their equations are included separately), but with a check to make sure the observed variables actually need including. Or if its better to unfurl any observed variables that are used in the RHS.

SciML / ModelingToolkit.jl

BifurcationProblem drops observed variables from ODESystem #2889