Figure 6

Comparing resilience against injury between plastic and non-plastic delays. Injury towards the connection topology \(a_{ij}\) is introduced at \(t_{\mathrm{inj}} = 160~\text{s}\) (red line). A. Plots of the connection matrix \(A = (a_{ij})\) before injury (\(\gamma = 0\)) and after injury (\(\gamma = 0.8\)), with \(a_{ij} = 1, 0\) indicated in white, black, respectively. B. The log histogram plots of delays at initial time \(t = 0~\text{s}\) (purple), midtime before injury \(t = 160~\text{s}\) (green), and at the end time following injury \(t = 320~\text{s}\) (red). The delays become distributed away from \(\tau _{ij} = \tau ^{0}\) to either some largely varying equilibrium delays \(\tau _{ij}^{E} > 0\) or decay to 0. Following injury, there are fewer delays available to stabilize the synchronous network. C, D. Plots of derivatives \(\theta _{i}'(t)\) over time, without and with plasticity, respectively. Both networks entrain in frequency pre-injury. Following injury, both networks entrain to a new frequency closer to \(\omega _{0}\). E, F. Plots of \(\sin \widehat {\phi}_{i}(t)\) over time, without and with plasticity, respectively. Following injury, the oscillators with plastic delays are able to coherently phase-lock within close proximity to each other, while the network without plastic delays remain in a non-convergent state. The parameters used were \(N = 50\), \(\varepsilon =0.01\), \(\alpha _{\tau }= 1.0\), \(g = 1.5\), \(\kappa = 80\), \(\omega _{0} = 1.0\), and \(\tau ^{0} = 2.0~\text{s}\)