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Frequency Response and Gap Tuning for Nonlinear Electrical Oscillator Networks

Figure 10

Erdös-Rényi random graph results.

From left to right, we present results for Erdös-Rényi random graphs with , , , and nodes. For each graph, we use algorithm (36) to modify the inductances such that the ratio of the smallest to the second smallest eigenvalue is . We use pre and post to denote, respectively, the graphs before and after algorithm (36) is applied. By shrinking the gap between the first two eigenvalues, the energy transferred to higher harmonics (37) can be increased to % (depending on the graph size), and the maximum voltage (38) can be increased to (depending on the graph size). The results for Erdös-Rényi graphs are much more strongly dependent on the number of nodes than the results shown in Figures 8 or 9. Note that the peak voltages for the graphs with forcing amplitude are the largest voltages for any graphs considered in this paper. We can increase the peak voltages for smaller graphs by choosing a smaller value of the conductance than (for all nodes ), the value used to compute the results in this figure.

doi: https://doi.org/10.1371/journal.pone.0078009.g010