Stability and Hopf-Bifurcating Periodic Solution for Delayed Hopfield Neural Networks with n Neuron

Figure 3

Time histories (a1, b1, and c1) and phase trajectories (a2, b2, and c2) of system (3) before, during, and after Andronov-Hopf bifurcation. In (a1) and (a2), 𝜏=0.193814883934925<0.213814883934925=𝜏^∗, and then the origin is locally asymptotically stable. In (b1) and (b2), 𝜏=0.213814883934925=𝜏^∗, and then there exists a periodic solution near the origin. In (c1) and (c2), 𝜏=0.233814883934925>0.213814883934925=𝜏^∗, and then there also exists a periodic solution near the origin, which implies that the origin is unstable (Example 3).