Figure 6

The stability of periodic solutions of system ( 4 ). (a)-(b) Time series. (c) Phase portrait. The parameters are the same as given in Figure 5. Numerical simulation shows that for system (4) the positive equilibrium point \(E^{*}\) is unstable for \(\tau= 0.59 >\hat{\tau} = 0.4422694125\) and the periodic phenomenon caused by a Hopf bifurcation occurs. There exists a positive period-1 solution of system (4).