2023/11/07 by Radost Waszkiewicz, Waszkiewicz, Radost, John Shaw +5
Computer Science · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.2311.03958
openalex publication_date 2023/11/07 · openalex created_date 2023/11/09 · openalex updated_date 2026/07/28
Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a complete stability analysis of the dynamical behaviour of any loop formed by fluctuating flows. We find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing mapped to constant and fluctuating components. Loops require fluctuation in the relative size of the flux between nodes, not just a temporal variation in the flux at a given node. Hence, there is both a minimum and a maximum amount of fluctuation relative to the constant-flux component where loops are supported.