Fig. 5

Bifurcation diagram of (11) and (12) for \(a=10\), \(b=9\), \(c=6\), \(d=1\), \(v_{\mathrm{th}}^{\mathrm{I}}=-2.5\), \(\lambda^{\mathrm{E}}=1\), \(\lambda^{\mathrm{I}}=1\), \(f_{\max}=1\), and \(\gamma=1\) with \(v_{\mathrm{th}}^{\mathrm{E}}\) 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 \(v^{\mathrm{E}}_{\mathrm{th}}=-1.6\) where the single asymptotically stable equilibrium point becomes unstable and gives rise to a stable limit cycle. At \(v^{\mathrm{E}}_{\mathrm{th}}=0.6\), the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears