Topological properties play a crucial role in the collective dynamics of coupled oscillators. In this Letter, we reveal a topology-induced phenomenon, including sparsity-induced stochastic resonance (SR) and coherence resonance (CR), in coupled noisy networks. The network sparsity alters the stochastic switching rates in coupled bistable systems and modulates the mean-field coherence in coupled excitable systems. The responses achieve maxima or minima at moderate sparsity (i.e., the optimal sparsity), implying the occurrence of sparsity-induced SR and CR. In particular, we discover the existence of invariant sparsity (domain) regarding sparsity-induced SR (CR). When the system size exceeds a threshold, the optimal sparsity (domain) is invariant with respect to system size, the five types of networks, and the frequency of the periodic force. By introducing a sparsity-dependent effective coupling, mean-field theory predicts sparsity-induced SR. These findings provide new insight into the collective dynamics of brain networks, especially explaining the pruning of neural connections by astrocytes.

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• Collective dynamics
• Coupled oscillators
• Neuronal dynamics
• Stochastic resonance
• Networks & random structures
• Small-world networks
• Monte Carlo methods