\label{sec:appendix_params}
\label{sec:type-i}
\(v_{{\rm Na}} = 1\), \(g_{{\rm Na}}= 1\), \(v_{\mathrm{K}}= -0.7\), \(g_{\mathrm{K}}= 2\), \(v_{{\mathrm{leak}}}= -0.5\), \(g_{{\mathrm{leak}}}= 0.5\), \(\beta_{{\rm K}} = 0.17\), \(I_{\rm app}= 0\), \(\gamma_{{\rm Na}} = 2.5\), \(\kappa_{{\rm Na}}= 0.025\), \(\gamma_{{\rm K}}= -3.45\), \(\kappa_{{\rm K}}= 0.76\), \(M = 200\), \(N = 1\).
\label{sec:type-i-with}
\(v_{{\rm Na}} = 1.15\), \(g_{{\rm Na}}= 1\), \(v_{\mathrm{K}}= -0.55\), \(g_{\mathrm{K}}= 2\), \(v_{{\mathrm{leak}}}= -0.35\), \(g_{{\mathrm{leak}}}= 0.5\), \(\beta_{{\rm K}} = 0.25\), \(I_{\rm app}= 0.01\), \(\gamma_{{\rm Na}} = 2.27\), \(\kappa_{{\rm Na}}= -0.32\), \(\gamma_{{\rm K}}= -10\), \(\kappa_{{\rm K}}= 1.78\), \(M = 200\), \(N = 3\).
\label{sec:type-ii}
\(v_{{\rm Na}} = 3.7\), \(g_{{\rm Na}}= 0.22\), \(v_{\mathrm{K}}= -0.9\), \(g_{\mathrm{K}}= 0.4\), \(v_{{\mathrm{leak}}}= -0.36\), \(g_{{\mathrm{leak}}}= 0.1\), \(\beta_{{\rm K}} = 0.04\), \(I_{\rm app}= 0.06\), \(\gamma_{{\rm Na}} = 1.22\), \(\kappa_{{\rm Na}}= -1.188\), \(\gamma_{{\rm K}}= -0.8\), \(\kappa_{{\rm K}}= 0.8\), \(M = 40\), \(N = 40\).