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NetworkDynamics.jl – composing and simulating complex networks in Julia. (English) Zbl 1465.37003

Summary: NetworkDynamics.jl is an easy-to-use and computationally efficient package for simulating heterogeneous dynamical systems on complex networks, written in Julia, a high-level, high-performance, dynamic programming language. By combining state-of-the-art solver algorithms from DifferentialEquations.jl with efficient data structures, NetworkDynamics.jl achieves top performance while supporting advanced features such as events, algebraic constraints, time delays, noise terms, and automatic differentiation.
©2021 American Institute of Physics

MSC:

37-04 Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory
37M05 Simulation of dynamical systems
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[1] Anvari, M.; Hellmann, F.; Zhang, X., Introduction to focus issue: Dynamics of modern power grids, Chaos, 30, 063140 (2020)
[2] Baldi, P.; Atiya, A. F., How delays affect neural dynamics and learning, IEEE Trans. Neural Netw., 5, 612-621 (1994)
[3] Bassett, D. S.; Sporns, O., Network neuroscience, Nat. Neurosci., 20, 353-364 (2017)
[4] Boguá, M., Pastor-Satorras, R., and Vespignani, A., “Epidemic spreading in complex networks with degree correlations,” in Statistical Mechanics of Complex Networks (Springer, 2003), pp. 127-147. · Zbl 1132.92338
[5] Menck, P. J.; Heitzig, J.; Kurths, J.; Schellnhuber, H. J., How dead ends undermine power grid stability, Nat. Commun., 5, 3969 (2014)
[6] Schultz, P.; Heitzig, J.; Kurths, J., Detours around basin stability in power networks, New J. Phys., 16, 125001 (2014)
[7] Pecora, L. M.; Carroll, T. L., Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80, 2109 (1998)
[8] Börner, R.; Schultz, P.; Ünzelmann, B.; Wang, D.; Hellmann, F.; Kurths, J., Delay master stability of inertial oscillator networks, Phys. Rev. Res., 2, 023409 (2020)
[9] Menck, P. J.; Heitzig, J.; Marwan, N.; Kurths, J., How basin stability complements the linear-stability paradigm, Nat. Phys., 9, 89-92 (2013)
[10] Lindner, M.; Hellmann, F., Stochastic basins of attraction and generalized committor functions, Phys. Rev. E, 100, 022124 (2019)
[11] Gelbrecht, M.; Kurths, J.; Hellmann, F., Monte Carlo basin bifurcation analysis, New J. Phys., 22, 033032 (2020)
[12] Zhang, X.; Hallerberg, S.; Matthiae, M.; Witthaut, D.; Timme, M., Fluctuation-induced distributed resonances in oscillatory networks, Sci. Adv., 5, eaav1027 (2019)
[13] Plietzsch, A.; Auer, S.; Kurths, J.; Hellmann, F.
[14] Rothkegel, A.; Lehnertz, K., Conedy: A scientific tool to investigate complex network dynamics, Chaos, 22, 013125 (2012) · Zbl 1331.37004
[15] Ansmann, G., Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE, Chaos, 28, 043116 (2018) · Zbl 1390.34005
[16] Clewley, R., Hybrid models and biological model reduction with PyDSTool, PLoS Comput. Biol., 8, e1002628 (2012)
[17] Bezanson, J.; Edelman, A.; Karpinski, S.; Shah, V. B., Julia: A fresh approach to numerical computing, SIAM Rev., 59, 65-98 (2017) · Zbl 1356.68030
[18] Rackauckas, C.; Nie, Q., DifferentialEquations.jl—A performant and feature-rich ecosystem for solving differential equations in Julia, J. Open Res. Softw., 5, 15 (2017)
[19] Rackauckas, C., “A comparison between differential equation solver suites in MATLAB, R, Julia, Python, C, Mathematica, Maple, and Fortran” (2020).
[20] See https://github.com/JuliaGraphs/LightGraphs.jl for the Julia package LightGraphs.jl.
[21] Rackauckas, C.; Innes, M.; Ma, Y.; Bettencourt, J.; White, L.; Dixit, V.
[22] Rackauckas, C.; Ma, Y.; Martensen, J.; Warner, C.; Zubov, K.; Supekar, R.; Skinner, D.; Ramadhan, A.
[23] Kittel, T., Auer, S., and Horn, C., “Sneak preview: PowerDynamics.jl—An open-source library for analyzing dynamic stability in power grids with high shares of renewable energy,” in 17th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as on Transmission Networks for Offshore Wind Plants (Energynautics GmbH, 2018).
[24] Plietzsch, A.; Kogler, R.; Auer, S.; Merino, J.; Gil-de Muro, A.; Liße, J.; Vogel, C.; Hellmann, F.
[25] Liemann, S., Strenge, L., Schultz, P., Hinners, H., Porst, J., Sarstedt, M., and Hellmann, F., “Probabilistic stability assessment for dynamic active distribution grids,” in IEEE Madrid PowerTech 2021 (IEEE, 2020).
[26] Schmietendorf, K.; Peinke, J.; Kamps, O., The impact of turbulent renewable energy production on power grid stability and quality, Eur. Phys. J. B, 90, 222 (2017)
[27] Anvari, M.; Werther, B.; Lohmann, G.; Wächter, M.; Peinke, J.; Beck, H.-P., Suppressing power output fluctuations of photovoltaic power plants, Solar Energy, 157, 735-743 (2017)
[28] Schäfer, B.; Witthaut, D.; Timme, M.; Latora, V., Dynamically induced cascading failures in power grids, Nat. Commun., 9, 1 (2018)
[29] Prior to Julia v1.5, creating standard views allocated memory on the heap.
[30] Kuramoto, Y., “Self-entrainment of a population of coupled non-linear oscillators,” in International Symposium on Mathematical Problems in Theoretical Physics (Springer, 1975), pp. 420-422. · Zbl 0335.34021
[31] Kuramoto, Y., Chemical Oscillations, Waves, and Turbulence (2003), Courier Corporation
[32] Rodrigues, F. A.; Peron, T. K. D.; Ji, P.; Kurths, J., The Kuramoto model in complex networks, Phys. Rep., 610, 1-98 (2016) · Zbl 1357.34089
[33] Simpson-Porco, J. W.; Dörfler, F.; Bullo, F., Synchronization and power sharing for droop-controlled inverters in islanded microgrids, Automatica, 49, 2603-2611 (2013) · Zbl 1364.93544
[34] Maistrenko, Y. L.; Lysyansky, B.; Hauptmann, C.; Burylko, O.; Tass, P. A., Multistability in the Kuramoto model with synaptic plasticity, Phys. Rev. E, 75, 066207 (2007)
[35] Watts, D. J.; Strogatz, S. H., Collective dynamics of ‘small-world’ networks, Nature, 393, 440-442 (1998) · Zbl 1368.05139
[36] See https://github.com/PIK-ICoN/NetworkDynamics.jl/blob/master/examples/paper.jl for a Julia script containing the code examples of this article.
[37] See https://github.com/SciML/StochasticDiffEq.jl for the Julia package StochasticDiffEq.jl.
[38] See https://github.com/SciML/StochasticDelayDiffEq.jl for the Julia package StochasticDelayDiffEq.jl.
[39] Datseris, G., DynamicalSystems.jl: A Julia software library for chaos and nonlinear dynamics, J. Open Source Softw., 3, 598 (2018)
[40] Ma, Y.; Gowda, S.; Anantharaman, R.; Laughman, C.; Shah, V.; Rackauckas, C.
[41] Dormand, J. R.; Prince, P. J., A family of embedded Runge-Kutta formulae, J. Comput. Appl. Math., 6, 19-26 (1980) · Zbl 0448.65045
[42] Hairer, E., Nørsett, S. P., and Wanner, G., Solving Ordinary Differential Equations I: Nonstiff Problems, Springer Series in Computational Mathematics No. 8, 2nd ed. (Springer, Heidelberg, 2009). · Zbl 1185.65115
[43] Hairer, E. and Wanner, G., Solving Ordinary Differential Equations II, Springer Series in Computational Mathematics (Springer, Berlin, 1996), Vol. 14. · Zbl 0859.65067
[44] See https://github.com/JuliaLang/PackageCompiler.jl for the Julia package PackageCompiler.jl.
[45] Kovacs, R.; Seufert, A.; Wall, L.; Chen, H.-T.; Meinel, F.; Müller, W.; You, S.; Brehm, M.; Striebel, J.; Kommana, Yannis, Y., Trussfab: Fabricating sturdy large-scale structures on desktop 3d printers, Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems (ACM, 2017)
[46] Hellmann, F.; Lindner, M., NetworkDynamics.jl
[47] Lincoln, L., Drauschke, F., Koulen, J., Monika, J., and Lindner, M., “NetworkDynamicsBenchmarks,” V.010.
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