Fazli Davood, Azimi-Tafreshi Nahid
Physics Department, Institute for Advanced Studies in Basic Sciences, Zanjan 45137-66731, Iran.
Phys Rev E. 2022 Jan;105(1-1):014303. doi: 10.1103/PhysRevE.105.014303.
Fixed-energy sandpile (FES) models, introduced to understand the self-organized criticality, show a continuous phase transition between absorbing and active phases. In this work, we study the dynamics of the deterministic FES models on random networks. We observe that close to absorbing transition the density of active nodes oscillates and nodes topple in synchrony. The deterministic toppling rule and the small-world property of random networks lead to the emergence of sustained oscillations. The amplitude of oscillations becomes larger with increasing the value of network randomness. The bifurcation diagram for the density of active nodes is obtained. We use the activity-dependent rewiring rule and show that the interplay between the network structure and the FES dynamics leads to the emergence of a bistable region with a first-order transition between the absorbing and active states. Furthermore during the rewiring, the ordered activation pattern of the nodes is broken, which causes the oscillations to disappear.
为理解自组织临界性而引入的固定能量沙堆（FES）模型，展示了吸收相和活跃相之间的连续相变。在这项工作中，我们研究了随机网络上确定性FES模型的动力学。我们观察到，接近吸收转变时，活跃节点的密度会振荡，且节点会同步倒塌。确定性的倒塌规则和随机网络的小世界特性导致了持续振荡的出现。随着网络随机性值的增加，振荡幅度会变大。得到了活跃节点密度的分岔图。我们使用与活动相关的重新布线规则，并表明网络结构与FES动力学之间的相互作用导致了一个双稳态区域的出现，该区域在吸收态和活跃态之间存在一阶转变。此外，在重新布线过程中，节点的有序激活模式被打破，这导致振荡消失。
