Emergence of oscillations in fixed energy sandpile models on complex networks

TL;DR

This paper investigates how deterministic fixed-energy sandpile models on complex networks exhibit oscillations and phase transitions, revealing the influence of network structure and rewiring on system dynamics.

Contribution

It demonstrates the emergence of sustained oscillations and bistability in FES models on random networks, highlighting the role of network randomness and rewiring.

Findings

Oscillations occur near the absorbing transition with synchronized node toppling.

Increasing network randomness amplifies oscillation amplitude.

Rewiring disrupts oscillations and induces a first-order phase transition.

Abstract

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.