A chaotic system of interconnected maps does not become more disorderly as you add more links.
Standard intuition says that the more links you add to a complex network, the more chaotic and messy it should become. These coupled chaotic maps on circulant graphs prove that theory wrong. Symmetry within the network structure cancels out the expected increase in entropy production. Even as the connectivity grows, the system remains at a constant level of complexity. This discovery helps researchers understand how to design networks that stay stable despite having many interlocking parts.
Coupled Arnol'd cat maps on circulant graphs
arXiv · 2605.00965
This paper investigates the chaotic properties of Arnol'd cat maps (ACMs) coupled on the nodes of a circulant graph. By demanding that the system's evolution matrix be symplectic, we determine the coupling matrix, which is naturally interpreted as the adjacency matrix of a circulant graph. Specifically, the study analyses the system's Lyapunov spectra and Kolmogorov-Sinai (K-S) entropy. Numerical simulations yield the counterintuitive result that the entropy production does not increase as the c