Tipping prediction of a class of large-scale radial-ring neural networks.

Understanding the emergence and evolution of collective dynamics in large-scale neural networks remains a complex challenge. This paper seeks to address this gap by applying dynamical systems theory, with a particular focus on tipping mechanisms. First, we introduce a novel (n+mn)-scale radial-ring neural network and employ Coates' flow graph topological approach to derive the characteristic equation of the linearized network. Second, through deriving stability conditions and predicting the tipping point using an algebraic approach based on the integral element concept, we identify critical factors such as the synaptic transmission delay, the self-feedback coefficient, and the network topology. Finally, we validate the methodology's effectiveness in predicting the tipping point. The findings reveal that increased synaptic transmission delay can induce and amplify periodic oscillations. Additionally, the self-feedback coefficient and the network topology influence the onset of tipping points. Moreover, the selection of activation function impacts both the number of equilibrium solutions and the convergence speed of the neural network. Lastly, we demonstrate that the proposed large-scale radial-ring neural network exhibits stronger robustness compared to lower-scale networks with a single topology. The results provide a comprehensive depiction of the dynamics observed in large-scale neural networks under the influence of various factor combinations.