Strange Attractors in Complex Networks

Abstract

Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean architectures with hidden symmetries, hinting at spontaneous order. Finding low-dimensional embeddings that reveal network patterns and link them to dimensionality that governs universal behavior remains a fundamental open challenge, as it needs to bridge the gap between microscopic disorder and macroscopic regularities. Here, the minimal space revealing key network properties is introduced, showing that non-integer dimensions produce chaotic-like attractors.

5 pages, 4 figures, and Supplemental Material. Accepted in Phys. Rev. E