Spontaneous Energy Migration and Self-Organized Evacuation in a Constraint Network Dynamical System

This paper reports a spontaneous energy migration phenomenon discovered in a constraint network dynamical system. When the local constraint network density exceeds a critical value, the system, without any external intervention and driven solely by the internal density gradient, spontaneously produces directional migration of energy units from high-density regions to low-density regions, thereby effectively alleviating local encryption runaway. This paper presents the complete emergence process of this phenomenon through numerical simulation and provides the quantitative relationship between migration rate and density gradient. The results show that in a system with an initial density ratio as high as 100:1, after 5000 steps of evolution, the central density drops from 0.80 to 0.31, and the peripheral density rises from 0.008 to 0.026. Of the 20 tracked central initial energy units, 17 successfully migrated to the periphery. A small number of high-energy heavy units remained stranded in the central region for the long term. This paper reports solely as an emergent self-organized phenomenon in nonlinear dynamics, without involving any theoretical explanation or engineering application.