Estimating Topology of Networks

We suggest a method for estimating the topology of a network based on the dynamical evolution supported on the network. Our method is robust and can be also applied when disturbances and/or modeling errors are presented. Several examples with networks of phase oscillators, pulse-coupled Hindmarch-Rose neurons, and Lorenz oscillators are provided to illustrate our approach.

Figure 1

Topology estimation of a network of $n=10$ phase oscillators: $b_{1,2}$ and $b_{6,2}$ vs time.

Figure 2

Topology estimation of a network of HR oscillators: $b_{7,2}$ and $b_{10,2}$ vs time.

Figure 3

Topology estimation of a network of 16 nonidentical Lorenz oscillators: $b_{1,j}+j$ vs time, for $j=1,2,\dots ,16$.

Figure 4

Monitoring the connection between the fifth and the 11th node: $b_{5,11}$ ($b_{11,5}$) vs time.

Figure 5

Topology estimation with uncertainty: the connection topology of a subnetwork. $b_{1,j}$ vs time for the subnetwork of 16 oscillators.