GitHub

BifurcationKit.jl

This Julia package aims at performing automatic bifurcation analysis of possibly large dimensional equations F(u, λ)=0 where λ is real by taking advantage of iterative methods, dense / sparse formulation and specific hardwares (e.g. GPU).

It incorporates continuation algorithms (PALC, deflated continuation, ...) based on a Newton-Krylov method to correct the predictor step and a Matrix-Free/Dense/Sparse eigensolver is used to compute stability and bifurcation points.

Despite initial focus on large scale problems, the package can easily handle low dimensional problems.

The package can also seek for periodic orbits of Cauchy problems . It is by now, one of the only softwares which provides shooting methods and methods based on finite differences or collocation to compute periodic orbits.

Hence, it is possible to study large scale nonlinear problems on different hardwares.

One design choice is that we try not to require u to be a subtype of an AbstractArray as this would forbid the use of spectral methods like the one from ApproxFun.jl. For now, our implementation does not allow this for all methods of the package.

Installation

This package requires Julia >= v1.3.0 because of the use of methods added to abstract types (see #31916).

To install it, please run

] add BifurcationKit

To install the bleeding edge version, please run

] add BifurcationKit#master

Citing this work

If you use this package for your work, we ask that you cite the following paper!! Open source development strongly depends on this. It is referenced on HAL-Inria as follows:

@misc{veltz:hal-02902346,
  TITLE = {{BifurcationKit.jl}},
  AUTHOR = {Veltz, Romain},
  URL = {https://hal.archives-ouvertes.fr/hal-02902346},
  INSTITUTION = {{Inria Sophia-Antipolis}},
  YEAR = {2020},
  MONTH = Jul,
  KEYWORDS = {pseudo-arclength-continuation ; periodic-orbits ; floquet ; gpu ; bifurcation-diagram ; deflation ; newton-krylov},
  PDF = {https://hal.archives-ouvertes.fr/hal-02902346/file/354c9fb0d148262405609eed2cb7927818706f1f.tar.gz},
  HAL_ID = {hal-02902346},
  HAL_VERSION = {v1},
}

Other softwares

There are many good softwares already available.

  • For continuation in small dimension, most softwares are listed on DSWeb. One can mention the widely used AUTO-07p, or also, XPPAUT, MATCONT, PyDSTool and COCO. All these are very reliable and some address high codimensional bifurcations.

  • For large scale problems, there is the versatile and feature full pde2path but also Trilinos-LOCA, CL_MATCONTL, COCO, GetFEM and the python libraries pyNCT and pacopy. There are also some nice lectures by D. Avitabile et al. on matrix free secant continuation based on a concise Matlab implementation which are used in the influential paper [Rankin]. At the time of initial release of BifurcationKit.jl, these lectures provided one of the only libraries for matrix-free continuation, much easier to use than Trilinos-LOCA.

  • For deflated continuation, there is defcont (by the inventor of the algo. P. E. Farrell) and this code by N. M. Evstigneev.

In Julia, we have the following tools:

A word on performance

The tutorials have not all been written with the goal of performance but rather simplicity (except maybe 2d Ginzburg-Landau equation and Langmuir–Blodgett model). One could surely turn them into more efficient codes. The intricacies of PDEs make the writing of efficient code highly problem dependent and one should take advantage of every particularity of the problem under study.

Requested methods for custom arrays

Needless to say, if you use "regular" arrays, you don't need to worry about what follows.

We make the same requirements as KrylovKit.jl. Hence, we refer to its docs and the vector-like interface for more information. We additionally require the following methods to be available:

  • Base.length(x): it is used in the constraint equation of the pseudo arclength continuation method (see continuation for more details). If length is not available for your "vector", define length(x) = 1 and adjust the parameter θ in PALC.
  • Base.copyto!(dest, in) this is required to reduce the allocations
  • Base.eltype must be extended to your vector type.

Citations

The papers citing this work are collected on google scholar.

Reproducibility

The documentation of BifurcationKit was built using these direct dependencies,
Status `~/work/BifurcationKitDocs.jl/BifurcationKitDocs.jl/docs/Project.toml`
  [1520ce14] AbstractTrees v0.4.5 `~/.julia/dev/AbstractTrees`
  [49cd1f3c] AsymptoticNumericalMethod v0.2.0
  [aae01518] BandedMatrices v1.7.5 `~/.julia/dev/BandedMatrices`
  [0f109fa4] BifurcationKit v0.4.2
  [52551710] BifurcationKitDocs v0.2.6 `~/work/BifurcationKitDocs.jl/BifurcationKitDocs.jl`
  [0c46a032] DifferentialEquations v7.14.0
  [e30172f5] Documenter v1.7.0
  [a106ebf2] DocumenterDiagrams v1.0.0
  [f6369f11] ForwardDiff v0.10.36
⌅ [961ee093] ModelingToolkit v8.76.0
  [d96e819e] Parameters v0.12.3
  [91a5bcdd] Plots v1.40.8
  [295af30f] Revise v3.5.18
  [0bca4576] SciMLBase v2.52.2
  [efcf1570] Setfield v1.1.1
  [47a9eef4] SparseDiffTools v2.20.0
  [37e2e46d] LinearAlgebra
  [2f01184e] SparseArrays v1.10.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
and using this machine and Julia version.
Julia Version 1.10.5
Commit 6f3fdf7b362 (2024-08-27 14:19 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_DEBUG = Documenter
A more complete overview of all dependencies and their versions is also provided.
Status `~/work/BifurcationKitDocs.jl/BifurcationKitDocs.jl/docs/Manifest.toml`
  [47edcb42] ADTypes v1.7.1
  [a4c015fc] ANSIColoredPrinters v0.0.1
  [1520ce14] AbstractTrees v0.4.5 `~/.julia/dev/AbstractTrees`
  [7d9f7c33] Accessors v0.1.37
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
⌅ [7d9fca2a] Arpack v0.5.3
  [4fba245c] ArrayInterface v7.16.0
  [4c555306] ArrayLayouts v1.10.3
  [49cd1f3c] AsymptoticNumericalMethod v0.2.0
  [aae01518] BandedMatrices v1.7.5 `~/.julia/dev/BandedMatrices`
  [0f109fa4] BifurcationKit v0.4.2
  [52551710] BifurcationKitDocs v0.2.6 `~/work/BifurcationKitDocs.jl/BifurcationKitDocs.jl`
  [e2ed5e7c] Bijections v0.1.9
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.1.0
  [764a87c0] BoundaryValueDiffEq v5.9.1
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [d360d2e6] ChainRulesCore v1.24.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [da1fd8a2] CodeTracking v1.3.6
  [944b1d66] CodecZlib v0.7.6
  [35d6a980] ColorSchemes v3.26.0
  [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 v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
⌅ [187b0558] ConstructionBase v1.5.6
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [bcd4f6db] DelayDiffEq v5.48.1
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.155.0
⌅ [459566f4] DiffEqCallbacks v2.37.0
  [77a26b50] DiffEqNoiseProcess v5.23.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.14.0
  [a0c0ee7d] DifferentiationInterface v0.5.17
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.111
  [ffbed154] DocStringExtensions v0.9.3
  [e30172f5] Documenter v1.7.0
  [a106ebf2] DocumenterDiagrams v1.0.0
⌅ [5b8099bc] DomainSets v0.6.7
⌅ [7c1d4256] DynamicPolynomials v0.5.7
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.7.8
  [6912e4f1] Espresso v0.6.2
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [c87230d0] FFMPEG v0.4.1
  [9d29842c] FastAlmostBandedMatrices v0.1.3
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.0.2
  [29a986be] FastLapackInterface v2.0.4
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.24.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.12
  [46192b85] GPUArraysCore v0.1.6
  [28b8d3ca] GR v0.73.7
  [c145ed77] GenericSchur v0.5.4
  [d7ba0133] Git v1.3.1
  [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 v0.3.24
  [b5f81e59] IOCapture v0.2.5
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.16
  [92d709cd] IrrationalConstants v0.2.2
  [42fd0dbc] IterativeSolvers v0.9.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.8
  [692b3bcd] JLLWrappers v1.6.0
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.60
  [aa1ae85d] JuliaInterpreter v0.9.35
  [ccbc3e58] JumpProcesses v9.13.7
  [ef3ab10e] KLU v0.6.0
⌅ [b3565e16] Kroki v0.2.0
  [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 v0.16.5
  [10f19ff3] LayoutPointers v0.1.17
  [0e77f7df] LazilyInitializedFields v1.2.2
  [5078a376] LazyArrays v2.2.1
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.3.0
  [7a12625a] LinearMaps v3.11.3
  [7ed4a6bd] LinearSolve v2.34.0
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.0.3
  [bdcacae8] LoopVectorization v0.12.171
  [6f1432cf] LoweredCodeUtils v3.0.1
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [d0879d2d] MarkdownAST v0.1.2
  [a3b82374] MatrixFactorizations v3.0.1
  [bb5d69b7] MaybeInplace v0.1.4
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [e1d29d7a] Missings v1.2.0
⌅ [961ee093] ModelingToolkit v8.76.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.6
  [d8a4904e] MutableArithmetics v1.4.6
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.14.0
  [6fe1bfb0] OffsetArrays v1.14.1
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.1.0
  [6ad6398a] OrdinaryDiffEqBDF v1.1.2
  [bbf590c4] OrdinaryDiffEqCore v1.5.1
  [50262376] OrdinaryDiffEqDefault v1.1.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.1.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.1.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.1.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.1.1
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.1.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.2.1
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.1.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.2.0
  [2d112036] OrdinaryDiffEqSDIRK v1.1.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.1.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.1.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [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 v1.40.8
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.0
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v3.27.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [2792f1a3] RegistryInstances v0.1.0
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [295af30f] Revise v3.5.18
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.52.2
  [c0aeaf25] SciMLOperators v0.3.10
  [53ae85a6] SciMLStructures v1.5.0
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.1.0
  [727e6d20] SimpleNonlinearSolve v1.12.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.20.0
  [0a514795] SparseMatrixColorings v0.4.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [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 v2.0.1
  [789caeaf] StochasticDiffEq v6.69.0
  [7792a7ef] StrideArraysCore v0.5.7
  [09ab397b] StructArrays v0.6.18
  [c3572dad] Sundials v4.25.0
  [2efcf032] SymbolicIndexingInterface v0.3.30
⌃ [19f23fe9] SymbolicLimits v0.2.1
⌅ [d1185830] SymbolicUtils v1.5.1
⌅ [0c5d862f] Symbolics v5.28.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
⌅ [92b13dbe] TaylorIntegration v0.15.3
  [6aa5eb33] TaylorSeries v0.18.1
  [62fd8b95] TensorCore v0.1.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [0796e94c] Tokenize v0.5.29
⌅ [3bb67fe8] TranscodingStreams v0.9.11
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.0
  [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
⌅ [68821587] Arpack_jll v3.5.1+1
  [6e34b625] Bzip2_jll v1.0.8+1
  [83423d85] Cairo_jll v1.18.0+2
  [ee1fde0b] Dbus_jll v1.14.10+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [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+1
  [d2c73de3] GR_jll v0.73.7+0
  [78b55507] Gettext_jll v0.21.0+0
  [f8c6e375] Git_jll v2.44.0+2
  [7746bdde] Glib_jll v2.80.2+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v8.3.1+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+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 v17.0.6+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 v3.0.15+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.54.1+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [629bc702] Qt6Declarative_jll v6.7.1+2
  [ce943373] Qt6ShaderTools_jll v6.7.1+1
  [e99dba38] Qt6Wayland_jll v6.7.1+1
⌅ [f50d1b31] Rmath_jll v0.4.3+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 v2.13.3+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 v0.53.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.43+1
  [f27f6e37] libvorbis_jll v1.3.7+2
  [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 v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
You can also download the "https://github.com/bifurcationkit/BifurcationKitDocs.jl/tree/gh-pages/v0.2.6/assets/Manifest.toml"">manifest file and the "https://github.com/bifurcationkit/BifurcationKitDocs.jl/tree/gh-pages/v0.2.6/assets/Project.toml"">project file.

References

  • Rankin

    J. Rankin et al., "Continuation of localized coherent structures in nonlocal neural field equations", SIAM J. Scientific Computing 36, pp. B70–B93 (2014): https://epubs.siam.org/doi/10.1137/130918721