Dynamical Systems in Neuroscience:

196 Bifurcations0.80.60.4stable limit cyclen-nullclineI=7limit cyclesnVIV-nullcline0.20-80 -60 -40 -20 0membrane voltage, mVI=4nodesaddlestable limit cyclestable limit cyclenodesaddleI=3.08homoclinic orbithomoclinic orbitnodesaddleI=1min/max of oscillations ofmembrane potential, mV0-20-40-60homoclinicbifurcationsaddlesnodeslimit cycles-800 2 4 6injected dc-current, InodesaddleFigure 6.28: Saddle homoclinic orbit bifurcation in the I Na,p +I K -model with parametersas in Fig. 4.1a and fast K + current (τ(V ) = 0.16). As the bifurcation parameter Idecreases, the stable limit cycle becomes a homoclinic orbit to a saddle.