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Stimulation to local areas remarkably affects brain activity patterns, which can be exploited to investigate neural bases of cognitive function and modify pathological brain statuses. There has been growing interest in exploring the fundamental action mechanisms of local stimulation. Nevertheless, how noise amplitude, an essential element in neural dynamics, influences stimulation-induced brain states remains unknown. Here, we systematically examine the effects of local stimulation by using a large-scale biophysical model under different combinations of noise amplitudes and stimulation sites. We demonstrate that noise amplitude nonlinearly and heterogeneously tunes the stimulation effects from both regional and network perspectives. Furthermore, by incorporating the role of the anatomical network, we show that the peak frequencies of unstimulated areas at different stimulation sites averaged across noise amplitudes are highly positively related to structural connectivity. Crucially, the association between the overall changes in functional connectivity as well as the alterations in the constraints imposed by structural connectivity with the structural degree of stimulation sites is nonmonotonically influenced by the noise amplitude, with the association increasing in specific noise amplitude ranges. Moreover, the impacts of local stimulation of cognitive systems depend on the complex interplay between the noise amplitude and average structural degree. Overall, this work provides theoretical insights into how noise amplitude and network structure jointly modulate brain dynamics during stimulation and introduces possibilities for better predicting and controlling stimulation outcomes. Author summary: Despite the extensive application of local stimulation in cognition research and disease treatments, how regional perturbations alter brain-wide dynamics has not yet been fully understood. Given that noninvasive stimulation is associated with changes in the signal-noise relationship, we assume that noise amplitude is one of the plausible factors modulating the stimulation effects. Using a whole-brain biophysical model under different stimulation sites and noise amplitudes, we explore the influence of noise amplitude on stimulation effects and, more importantly, the interplay between noise amplitude and network structure. From a regional perspective, noise amplitude reduces the peak frequencies in unstimulated areas during stimulation. Moreover, we find a high similarity between the noise-averaged peak frequency matrix and the structural network. From a network perspective, we show that the changes in functional connectivity are decreased by noise amplitude, while the alterations in structural constraints display nonmonotonic trends. Intriguingly, increasing the noise amplitude in specific ranges can improve the association between network-level effects and structural degree, promoting better predicting and controlling therapeutic performance. Finally, the behaviors of cognitive systems quantified by network-level effects are jointly modulated by the noise amplitude and average structural degree. [ABSTRACT FROM AUTHOR]