Bursting behavior in a non-smooth electric circuit

The dynamics of a non-smooth electric circuit with order gap between the natural frequency and the excitation frequency is investigated in this Letter. Different types of bursting phenomena can be observed in the numerical simulations. By assuming the forms of the solutions and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solutions is presented, which can also be used to account for the evolution of the complicated structures of the phase portraits with the variation of the parameters. Period-adding bifurcation has been explored on the computation of the eigenvalues related to the solutions. It is shown that, the multiple crossing bifurcation, which is the combination of the Hopf bifurcation and the turning point bifurcation, occurring at the non-smooth boundaries leads the periodic burster to the quasi-periodic oscillation.