Coupled Homogeneous Hopfield Neural Networks: Simplest Model Design, Synchronization, and Multiplierless Circuit Implementation

When using a synapse as a coupler to connect neurons, parameter-based synchronization transitions have been investigated. However, the dependence on initial conditions has not been comprehensively discussed in the literature. This work presents an electrical-synapse-coupled model consisting of two homogeneous Hopfield neural networks (HNNs), which is the simplest network-to-network coupling model known for HNN. The model possesses several fixed points, which are found to be unstable. Simulation results of peak differences, bifurcation diagrams, and normalized mean synchronization errors indicate that complex synchronization transitions occur, depending on both the electrical coupling strength and initial conditions. Particularly, we focus here on mapping the basins of attraction between periodic and chaotic synchronization for bistable patterns. Finally, a multiplierless electrical neuron circuit is developed to validate initial condition-induced synchronization phenomena, which provides a new perspective for the study of collective dynamics of brain-like networks and the development of lightweight neuromorphic circuits.