This paper focuses on the analysis of a third-order nonlinear amplitude equation for finding possible dynamical behavior appearing in the plasma torch. The analysis was achieved by employing system linearization and bifurcation theorems. Local bifurcation analysis for a class of the third-order nonlinear systems was studied in (Liaw et al, 2009) to solve for the existence conditions of pitchfork stationary bifurcation, Andronov-Hopf bifurcations, period-doubling, and torus bifurcation. Numerical simulations were also obtained to study the nonlocal dynamical phenomena and the linkage among bifurcation phenomena and chaotic behavior. In this paper, those analyses will be extended to the more general cases. The scenarios for the possible nonlinear behavior in a third-order amplitude equation are justified for the plasma torch with respect to the variation of system parameters via the numerical simulations, which might provide a guide to determine the occurrence of nonlinear phenomena in the practical application of the plasma torch.