Structural Stability of Spiking Neural Networks
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The past decades have witnessed an increasing interest in spiking neural networks (SNNs) due to their great potential of modeling time-dependent data. Many algorithms and techniques have been developed; however, theoretical understandings of many aspects of spiking neural networks are still cloudy. A recent work [Zhang et al. 2021] disclosed that typical SNNs could hardly withstand both internal and external perturbations due to their bifurcation dynamics and suggested that self-connection has to be added. In this paper, we investigate the theoretical properties of SNNs with self-connection, and develop an in-depth analysis on structural stability by specifying the lower and upper bounds of the maximum number of bifurcation solutions. Numerical experiments conducted on simulation and practical tasks demonstrate the effectiveness of the proposed results.
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