Before revision: We investigate the dynamical effects of non-Gaussian asymmetric stable L\'evy fluctuations on the evolution of the transcription factor activator in a genetic regulation system . The noisy fluctuations arise from the synthesis reaction rate .
After revision: We investigate the dynamical effects of non-Gaussian asymmetric stable L\'evy fluctuations on the evolution of the transcription factor activator in a genetic regulation system , when the synthesis reaction rate .