The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated. The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated. Time delay is selected as the bifurcation parameter, and sufficient conditions for stability and Hopf bifurcation are derived. It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model. Furthermore, a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented. Finally, the effectiveness of the theory is verified through simulation results.

The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated. The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated. Time delay is selected as the bifurcation parameter, and sufficient conditions for stability and Hopf bifurcation are derived. It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model. Furthermore, a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented. Finally, the effectiveness of the theory is verified through simulation results.