Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

16: Dynamical Networks I - Modeling

  • Page ID

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    • 16.1: Dynamical Network Models
      There are several different classes of dynamical network models.
    • 16.2: Simulating Dynamics on Networks
      Because NetworkX adopts plain dictionaries as their main data structure, we can easily add states to nodes (and edges) and dynamically update those states iteratively. This is a simulation of dynamics on networks. This class of dynamical network models describes dynamic state changes taking place on a static network topology.
    • 16.3: Simulating Dynamics of Networks
      Dynamics of networks models capture completely different kinds of network dynamics, i.e., changes in network topologies. This includes the addition and removal of nodes and edges over time. As discussed in the previous chapter, such dynamic changes of the system’s topology itself are quite unusual from a traditional dynamical systems viewpoint, because they would make it impossible to assume a well-defined static phase space of the system.
    • 16.4: Simulating Adaptive Networks
      The final class of dynamical network models is that of adaptive networks. It is a hybrid of dynamics on and of networks, where states and topologies “co-evolve,” i.e., they interact with each other and keep changing,  often over the same time scales.