First- and second-order network coherence in N-duplication weighted corona networks - Liu, Chao (Frontiers in Physics, 2025)
This paper studies first- and second-order coherence problems for N-duplication weighted corona networks subject to stochastic disturbances. Explicit expressions of the coherence for first-order (and second-order) dynamics, which are determined by the sum of the reciprocal (and square of reciprocal) of each nonzero eigenvalue of the Laplacian matrix, are derived. In particular, for both first- and second-order systems, the analytical formulas of the network coherence are presented from two different perspectives. Based on these formulas, the influence of the duplication N, the weight ω, and the factor networks G1 and G2 on the network coherence of the corona network G1◦G2 is investigated. Some noteworthy topological properties of the N-duplication weighted corona network are also revealed.