The nonlinear dynamical analysis of a rod-type plasma torch was presented in this paper. Local bifurcation analysis for a class of the third-order nonlinear systems was first studied to solve for the existence
conditions of both stationary and Andronov-Hopf bifurcations. It was then
applied to the dynamical analysis of the rod-type plasma torch. Both
analytical results and numerical simulations were found to agree with those obtained by Ghorui et al, (2000). Moreover, the scenarios for the possible nonlinear behavior in the plasma torch dynamics were also obtained with respect to the variation of system parameters via the numerical simulations,which might provide a guide for finding nonlinear phenomena in the practical application of the plasma torch.