2025/05/25 by Mohammad Jafari, Jafari, Mohammad
Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2505.19296
openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We investigate a network model in which a single random walker combines local diffusion with preferential resetting to previously visited nodes. Each arrival deposits one unit of stress on the target node, and threshold crossings trigger sandpile-like relaxation cascades. The fixed per-neighbor transfer rule produces a brittle transition on Watts--Strogatz networks: below the stress-balance condition αk ≃ T cascades remain short, whereas mildly supercritical transfer values generate runaway-capped events at large system sizes. A subtractive dissipative rule -- in which a toppling node loses T units and redistributes only βT across its neighbors -- stabilizes broad, finite cascades over a significantly wider parameter range. For β= 0.995 and 0.998, the dissipative model remains non-runaway through N = 4096 and favors power-law tails by AIC model selection; however, system-scale event fractions decrease with N, a branching-ratio proxy remains below unity, and bootstrap Kolmogorov--Smirnov tests reject a pure power law. Shuffled-order controls that preserve node-visit frequencies while randomizing the temporal sequence of arrivals yield nearly identical avalanche macrostatistics for β< 1 across memory strengths q = 0--0.6, demonstrating that dissipation and redistribution rules dominate over temporal memory ordering in the regime we can reliably characterize. On Barabási--Albert networks, fixed per-neighbor transfer is strongly hub-sensitive, while degree-normalized transfer suppresses runaways but yields distributions better described by exponentials. The central conclusion is therefore regime-based: memory-biased driving localizes stress injection and shapes visitation hotspots, but broad cascade behavior is governed primarily by stress balance, dissipation strength, and network topology.