Lu and Hamilton model for solar flares over a rewiring complex network

Abstract

We present a modified Lu \& Hamilton-type model where the neighborhood relations are replaced by topological connections, which can be dynamically altered. The model represents each grid node as a flux tube, as in the classic model, but with connections evolving to capture the complex effects of magnetic reconnection. Through this framework, we analyze how the dissipated energy distribution changes, particularly focusing on the power-law exponent $\alpha_E$, which decreases with respect to the original model due to rewiring effects. When the system is dominated by rewiring, it presents an exponential distribution exponent $\beta_E$, showing a faster decay of dissipated energy than in the original model. This leads to microflare-dominated dynamics at short timescales, causing the system to lose the scale-free behavior observed in both the original model (Lu \& Hamilton 1991) and in configurations where energy release is primarily driven by forcing rather than rewiring. Our results reveal a clear transition from power-law to exponential regimes as the rewiring probability increases, fundamentally altering the energy distribution characteristics of the system. In contrast, when considering topological neighbors instead of local ones, the model's dynamics become intrinsically nonlocal. This leads to scaling exponents comparable to those reported in other nonlocal dynamical systems.