Dynamics and Optimal Behavioral Strategies of Motile Networks

Network models play a key role in understanding connectivity and flow in diverse systems such as gene regulation, transportation, and ecosystems. Far less explored are networks that move through space. Here we investigate an understudied class of network models, i.e., trees where the network morphology can dynamically change while the overall mass (sum of all edge lengths) is conserved. We developed a simple mathematical model accounting for the branching, growth, and retraction rates, leading to a compact yet insightful phase space that reveals different optimal strategies for system behavior under different external constraints. We successfully apply this model to various natural and artificial systems, e.g., cellular chemotaxis, slime mold behavior, and businesses evolution – suggesting universal optimal behavioral strategies in motile network systems.