Tipping Prediction of a Class of Large-Scale Radial-Ring Neural Networks

Abstract

Understanding the emergence of collective dynamics in large-scale neural networks remains a challenging endeavor. This paper aims to address this gap by utilizing dynamic systems theory, particularly emphasizing tipping mechanisms. First of all, we introduce a novel $(n+mn)$-scale radial-ring neural network and utilize the topological approach of Coates' flow graph to determine the characteristic equation of the linearized network. Secondly, by deriving stability conditions and predicting the tipping point using the algebraic approach based on the integral element idea, we identify significant factors such as synaptic transmission delay, self-feedback coefficient, and network topology. Finally, we validate the effectiveness of the methodology in predicting the tipping point through numerical simulations. The simulations provide a thorough portrayal of the dynamics exhibited by large-scale neural networks, while also integrating robustness tests. This research contributes to a deeper understanding of the mechanisms underlying collective dynamics in large-scale neural networks, offering valuable insights for both theoretical frameworks and practical applications.

Keywords: Neural Networks, Tipping, Hopf bifurcation, Large-scale, Coates' flow graph