Fig. 9

Bifurcation diagram of (11) and (12) for \(a=10\), \(b=9\), \(c=6\), \(d=1\), \(v_{\mathrm{th}}^{\mathrm{E}}=-0.5\), \(v_{\mathrm{th}}^{\mathrm{I}}=-2.5\), \(\lambda^{\mathrm{E}}=1\), \(f_{\max}=1\), and \(\gamma=1\) with \(\lambda^{\mathrm{I}}\) as a bifurcation parameter. The solid line represents asymptotically stable equilibrium point, whereas the dashed line represents unstable equilibrium point. A supercritical Hopf bifurcation occurs at \(\lambda ^{\mathrm{I}}_{1}=0.85\) where the single asymptotically stable equilibrium point becomes unstable and gives rise to a stable limit cycle. At \(\lambda^{\mathrm{I}}_{2}=2.3\), the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears