NetworkDynamics
A package for working with dynamical systems on complex networks. NetworkDynamics.jl provides an interface between Graphs.jl and DifferentialEquations.jl. It allows for high performant simulation of dynamic networks by describing the local dynamics on the edges and vertices of the graph.
The behavior of a node or an edge can be described by algebraic equations, by differential algebraic equation (DAEs) in mass matrix form or by ordinary differential equations (ODE).
The central construction is the function Network that receives functions describing the local dynamics on the edges and nodes of a graph g as inputs, and returns a composite function compatible with the DifferentialEquations.jl calling syntax.
nd = Network(g, vertex_dynamics, edge_dynamics)
nd(dx, x, p, t)Main features:
- Clear separation of local dynamics and topology: you can easily change topology of your system or switching out dynamical components.
- High performance when working with heterogeneous models (which means heaving different local dynamics in different parts of your network).
- Symbolic Indexing into solutions and states: NetworkDynamics keeps track of the states of the individual subsystems.
- Different execution schemes: NetworkDynamics exploits the known inter-dependencies between components to auto parallelize execution, even on GPUs!
- Equation based models: use ModelingToolkit.jl to define local dynamics, use
NetworkDynamics.jlto combine them into large networks!
Where to begin?
Check out the Mathematical Model to understand the underlying modelling ideas of NetworkDynamics followed by the page on Network Construction to learn how to implement you own models.
If you prefer to look at some concrete code first check out the Getting Started tutorial!
Installation
Installation is straightforward with Julia's package manager.
(v1.11) pkg> add NetworkDynamicsReproducibility
Direct dependencies used for this documentation:
Status `~/work/NetworkDynamics.jl/NetworkDynamics.jl/docs/Project.toml`
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Info Packages marked with ⌃ have new versions available and may be upgradable.Julia Version:
Julia Version 1.11.2
Commit 5e9a32e7af2 (2024-12-01 20:02 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
LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eagerFull Manifest:
Status `~/work/NetworkDynamics.jl/NetworkDynamics.jl/docs/Manifest.toml`
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[38a345b3] Libuuid_jll v2.40.2+0
[856f044c] MKL_jll v2024.2.0+0
[e7412a2a] Ogg_jll v1.3.5+1
[18a262bb] OpenEXR_jll v3.2.4+0
[458c3c95] OpenSSL_jll v3.0.15+1
[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 v0.5.1+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 v2.13.5+0
[aed1982a] XSLT_jll v1.1.42+0
[ffd25f8a] XZ_jll v5.6.3+0
[f67eecfb] Xorg_libICE_jll v1.1.1+0
[c834827a] Xorg_libSM_jll v1.2.4+0
[4f6342f7] Xorg_libX11_jll v1.8.6+1
[0c0b7dd1] Xorg_libXau_jll v1.0.11+1
[935fb764] Xorg_libXcursor_jll v1.2.0+4
[a3789734] Xorg_libXdmcp_jll v1.1.4+1
[1082639a] Xorg_libXext_jll v1.3.6+1
[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+1
[c7cfdc94] Xorg_libxcb_jll v1.17.0+1
[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+1
[3161d3a3] Zstd_jll v1.5.6+1
[35ca27e7] eudev_jll v3.2.9+0
[214eeab7] fzf_jll v0.56.3+0
[1a1c6b14] gperf_jll v3.1.1+1
[9a68df92] isoband_jll v0.2.3+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 v1.6.44+0
[075b6546] libsixel_jll v1.10.3+1
[f27f6e37] libvorbis_jll v1.3.7+2
[c5f90fcd] libwebp_jll v1.4.0+0
[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 v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[8bf52ea8] CRC32c v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.11.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.11.0
[de0858da] Printf v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.11.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.6+0
[14a3606d] MozillaCACerts_jll v2023.12.12
[4536629a] OpenBLAS_jll v0.3.27+1
[05823500] OpenLibm_jll v0.8.1+2
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.7.0+0
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[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`Funding
Development of this project was in part funded by the German Federal Ministry for Economic Affairs and Climate Action as part of the OpPoDyn-Project (Project ID 01258425/1, 2024-2027).
