Multiple and Complete Stability of Recurrent Neural Networks With Sinusoidal Activation Function

This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.

Automated summary

This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function, including sufficient criteria for stability and estimation of attraction basins. In contrast to existing results, the new criteria are applicable for both finite and countably infinite numbers of equilibria.