Bursting phenomena as well as bifurcation mechanism in nonlinear circuit
非线性电路的簇发现象及分岔机制

By introducing time-dependent current source to Hartley model with cubic nonlinearity and choosing suitable values of parameter and excited frequency, we produce a periodically excited fast-slow electric circuit with two time-scales. The condition for the occurrence of Hopf bifurcation is used to derive the analytical expression of the first Lyapunov coefficient, which is validated by numerical simulation. The coefficient, as well as the bifurcation theory is employed to investigate the fast-slow effect in the system, which leads to the typical periodic bursting in the associated bifurcation modes. Based on the autonomous system and the transformed phase-portraits, the mechanism of the bursting phenomenon is presented from the standpoint of bifurcation.