Intelligent Control of Transportation Flow in Physarum Networks

The Physarum network expands or retracts in response to environmental stimuli, demonstrating an intelligent adaptive capability to locate optimal paths for nutrient transport. The underlying physical mechanism governing this intelligence behavior remains an unresolved problem in biological physics.unlike the unidirectional flow typical of urban traffic networks, cytoplasmic flow within the Physarum network exhibits periodic oscillations modulated by biological repellents and attractants. In this study, we investigate how local flows within the networks branch channels interact to collectively govern the global oscillatory dynamics.We find that the measured flow fluxes at intersection nodes obey Kirchhoff's current law. Phase differences exist among the flows in different branches.At the microscopic scale, flow distribution exhibits only brief periods of traffic congestion, which are resolved by the oscillatory flows. By mapping the flow flux vectors onto the magnetic moment vector of spin ice model, we demonstrate that the flow vectors strictly obey the ice-rule of vertex models in statistical physics.Notably, the three branches converging at a Y-shaped node never become blocked simultaneously, thereby preventing traffic congestion and ensuring efficient transmission of nutrients and signals.This intelligent flow control phenomenon offers novel insights for addressing traffic congestion and advances our understanding of frustrated quantum magnetism.