Fig. 10

Left: region of stability for a synchronised pair of identical IF neurons with inhibitory coupling and collective period \(T=\ln2\). The solid curve \(\vert \epsilon \vert = \epsilon _{c}(\alpha)\) denotes the boundary of the stability region. Crossing the boundary from below signals excitation of the linear mode \((1,-1)\) leading to a stable state in which one neuron becomes quiescent (oscillator death). For \(\alpha> \alpha_{0}\) the synchronous state is stable for all ϵ. The dashed curve denotes corresponds to the eigenvalue with \(\nu=1\). Right: plot of critical coupling \(\epsilon_{c}\) as a function of α for various network sizes N. The critical inverse rise time \(\alpha_{0}(N)\) is seen to be a decreasing function of N with \(\alpha _{0}(N)\rightarrow0\) as \(N\rightarrow\infty\)