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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.19296 |
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| _version_ | 1866918441777102848 |
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| author | Jafari, Mohammad |
| author_facet | Jafari, Mohammad |
| contents | 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 $αk \simeq T$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dissipative Avalanche Regimes Driven by Memory-Biased Random Walks on Networks Jafari, Mohammad Statistical Mechanics 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 $αk \simeq T$ 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. |
| title | Dissipative Avalanche Regimes Driven by Memory-Biased Random Walks on Networks |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2505.19296 |