Control of mediated stochastic resonance in multilayer neural networks

This study focuses on exploring noise-induced dynamics in multilayer neural networks consisting of FitzHugh–Nagumo (FHN) neurons. Initially, a two-layer neural network is established, where layer-1 is exposed to weak signal and noise while layer-2 remains unaffected. Our findings indicate that, with appropriate weak signal and noise levels in layer-1, inter-layer coupling enables the occurrence of stochastic resonance (SR) and double-SRs in layer-2. This phenomenon is explained, with emphasis on the crucial role played by the signal period and the inherent discharge period of layer-2 in generating double-SRs. Particularly, we uncover that by finely tuning the inter-layer coupling strength, a remarkable dynamic transition can be induced in layer-2: a shift from a single weak SR to weak double-SRs, followed by the manifestation of strong double-SRs, and ultimately culminating in a single strong SR. Furthermore, our research reveals that an optimal intra-layer coupling strength maximizes the SR in layer-1, whereas achieving the peak effect for double-SRs in layer-2 requires an optimal inter-layer coupling strength. Moreover, our investigation extends to a three-layer neural network, elucidating that SR in the layer, which is not directly connected to the layer with external inputs, can be well controlled through inter-layer coupling or intra-layer coupling.