Experiment and Analysis of Emergence Based on Gaussian Cloud Model

The cloud model provides a unified mathematical framework for representing both randomness and fuzziness simultaneously, offering an effective mathematical tool for modeling complex systems. This paper focuses on the emergent phenomenon of spontaneous synchronous flashing in fireflies and employs Gaussian cloud model theory to develop an initialization framework. Uncertainty is quantified using three core numerical characteristics of the cloud model—expectation, entropy, and hyperentropy—while a Gaussian potential function is adopted to characterize how interaction strength varies with spatial distance. A MATLAB-based simulation platform is developed to reproduce the emergent transition of fireflies from disordered flashing to synchronous behavior across different spatial domains. Our results demonstrate that group synchronization efficiency is strongly governed by the initial spatial configuration of individuals. Introducing driving nodes (special agents) can accelerate synchronization, but increasing their quantity yields diminishing marginal returns; the optimal strategy is a single special agent placed at the domain center. Collective emergence depends more strongly on the topological structure of inter-individual interactions than on the number of driving nodes. These findings confirm that interaction topology dominates synchronization performance over driving-node quantity, providing a theoretical basis for guiding unmanned swarm coordination with minimal control nodes.