Effects of external bounded noise on nonlinear dynamics of plasma density

Random fluctuations in electronic density can considerably influence the profile of the resonance and stability curves of a column plasma. The fluctuations affect the resonance in different ways depending on the order of the considered resonance. The purpose of this effort is to investigate the effects of bounded noise on the primary resonances of density fluctuation in plasma. Along these lines, the response and stability are considered and analyzed using both the method of multiple scales and stochastic averaging. Further, we unveil very interesting dynamic responses in the frequency response. The statistical moment is calculated and its stability condition established. Through numerical simulations, we show that the density perturbation may undergo hysteretic transitions induced by external noisy excitation. The response of the global system is affected by bounded noise as demonstrated through the Poincaré map.