In this paper, global bifurcations and chaotic dynamics under bounded noise perturbation for the nonlinear normalized radial electric field near plasma are investigated using the Melnikov method. From this analysis, we get criteria that could be useful for designing the model parameters so that the appearance of chaos could be induced (when heating particles) or run out for quiescent H-mode appearance. For this purpose, we use a test of chaos to verify our prediction. We find that, chaos could be enhanced by noise amplitude growing. The results of numerical simulations also reveal that noise intensity modifies the attractor size through power spectra, correlation function, and Poincaré map. The criterion from the Melnikov method which is used to analytically predict the existence of chaotic behavior of the normalized radial electric field in plasma could be a valid tool for predicting harmful parameters values involved in experiment on Tokamak L–H transition.