Jolakoski Petar, Trajanovski Pece, Pal Arnab, Stojkoski Viktor, Kocarev Ljupco, Sandev Trifce
Macedonian Academy of Sciences and Arts, Research Center for Computer Science and Information Technologies, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia.
Ss. Cyril and Methodius University in Skopje, Institute of Physics, Faculty of Natural Sciences and Mathematics, Arhimedova 3, 1000 Skopje, Macedonia.
Phys Rev E. 2025 Mar;111(3-1):034129. doi: 10.1103/PhysRevE.111.034129.
We study the effects of stochastic resetting on the reallocating geometric Brownian motion (RGBM), an established model for resource redistribution relevant to systems such as population dynamics, evolutionary processes, economic activity, and even cosmology. The RGBM model is inherently nonstationary and non-ergodic, leading to complex resource redistribution dynamics. By introducing stochastic resetting, which periodically returns the system to a predetermined state, we examine how this mechanism modifies RGBM behavior. Our analysis uncovers distinct long-term regimes determined by the interplay between the resetting rate, the strength of resource redistribution, and standard geometric Brownian motion parameters: the drift and the noise amplitude. Notably, we identify a critical resetting rate beyond which the self-averaging time becomes effectively infinite. In this regime, the first two moments are stationary, indicating a stabilized distribution of an initially unstable, mean-repulsive process. We demonstrate that optimal resetting can effectively balance growth and redistribution, reducing inequality in the resource distribution. These findings help us understand better the management of resource dynamics in uncertain environments.
我们研究了随机重置对重新分配几何布朗运动（RGBM）的影响，RGBM是一个已确立的资源再分配模型，与诸如种群动态、进化过程、经济活动乃至宇宙学等系统相关。RGBM模型本质上是非平稳且非遍历的，会导致复杂的资源再分配动态。通过引入随机重置，即定期将系统恢复到预定状态，我们研究了这种机制如何改变RGBM的行为。我们的分析揭示了由重置率、资源再分配强度以及标准几何布朗运动参数（漂移和噪声幅度）之间的相互作用所决定的不同长期状态。值得注意的是，我们确定了一个临界重置率，超过该临界值后，自平均时间实际上变为无穷大。在这种状态下，前两个矩是平稳的，这表明一个初始不稳定、均值排斥过程的分布趋于稳定。我们证明，最优重置可以有效地平衡增长和再分配，减少资源分配中的不平等。这些发现有助于我们更好地理解不确定环境中资源动态的管理。
