sho7014 / NetworkDynamics.jl

Julia package for working with Dynamics on Networks.

Fork of NetworkDynamics.jl modified to deal with non-diagonal noise.

A new vertex struct NonDiagonalSDEVertex(f!, dim, noise_dim::Int, slide::Int, mass_matrix, sym) is introduced.

• noise_dim is the number of components of noise in a vertex equation (vertex-wise Ito dimension). Only problems with homogeneous Ito dimesions are currently supported.
• slide controls how the non-diagonal noise is injected. if it is set zero, the noise is vertex-independent (common noise), while if it is set equals to noise_dim, the noise can be vertex-dependent.
  noise_rate_prototype of a SDEProblem should also be appropriately adjusted in accordance with whether the noise is shared or not. Consider a system of SDEs with N vertices for an example. If the noise is shared among vertices, noise_rate_prototype should be an array of size (N*dim, noise_dim), otherwise set it that of size (N*dim, N*noise_dim).

This is just a naive workaround, so its performance has not been examined and important features such as sparse arrays for noise_rate_prototype are not supported. (Sparse arrays for noise_rate_prototype is a bad idea, explained as Keep noise vectors dense #436.) The features which are not tested and hence might not be supported currently are as follows.

• Non-identity mass matrix
• ODEEdge
• DDEs (promotions are not defined)
• noise_rate_prototype option defined as other than normal Array
• Networks with heterogeneous Ito dimensions