Complete Dynamical Networks: Synchronization, Information Transmission and Topological Order - Rocha, J. Leonel; Carvalho, S. (Discontinuity, Nonlinearity, and Complexity, 2026)
The space of complete dynamical networks of systems with discontinuous piecewise linear maps is analyzed. The purpose of this paper is to investigate synchronizability and measures of information transmission in this complex network space. The network topologies are regular ring lattices which are characterized by circulant matrices and the conditional Lyapunov exponents are explicitly determined. The mutual information rate and the Kolmogorov-Sinai entropy are characterized and properties of these measures are proved, depending on the topological entropy of the local dynamics and on the synchronization interval. A topological order is defined and monotony properties between the network topological entropy, the mutual information rate and the Kolmogorov-Sinai entropy are established. Numerical simulations are provided to illustrate the theoretical results.