In this article, we evaluated the variations of the brain and muscle activations while subjects are exposed to different perturbations to walking and standing balance. Since EEG and EMG signals have complex structures, we utilized the complexity-based analysis. Specifically, we analyzed the fractal dimension and sample entropy of Electroencephalogram (EEG) and Electromyogram (EMG) signals while subjects walked and stood, and received different perturbations in the form of pulling and rotation (via virtual reality). The results showed that the complexity of EEG signals was higher in walking than standing as the result of different perturbations. However, the complexity of EMG signals was higher in standing than walking as the result of different perturbations. Therefore, the alterations in the complexity of EEG and EMG signals are inversely correlated. This analysis could be extended to investigate simultaneous variations of rhythmic patterns of other physiological signals while subjects perform different activities.