A multi-domain indicator framework for synchronization states classification in large-scale neural networks with distinct topologies

The regulation of synchronization in large-scale neural networks is fundamental to understanding brain function and advancing brain-inspired intelligence. However, a general and robust method for synchronization state discrimination across different topologies remains challenging to establish. In this work, a multi-domain indicator framework is first proposed to discriminate network states. Since its robustness of classification is compromised under multiple initial conditions, the corresponding voting strategy is further introduced to address this issue. First, the representative topologies, including Ring, ER, WS, BA, and Star, are constructed under a unified modeling framework, based on which a corresponding synchronization indicator system is further proposed. Then, as a special case, a two-neuron coupled system is examined to reveal how parameter mismatch modulates synchronization in small-scale networks. The voting-based synchronization classification strategy is subsequently applied to the five single-layer networks, through which topology is identified as the primary factor governing synchronization states. Furthermore, single-layer networks are further extended to two-layer and three-layer networks, where the modulatory role of interlayer connectivity patterns in synchronization is uncovered. These results demonstrate that the proposed framework effectively distinguishes synchronization states across varying topologies and layer configurations, and provides a reliable tool for analyzing collective behavior in complex neural networks.