Finite-Time Intra-Layer and Inter-Layer Quasi-Synchronization of Two-Layer Multi-Weighted Networks

The article pays attention to a two-layer multi-weighted network, and studies finite-time (FT) intra-/inter-layer quasi-synchronization of two-layer multi-weighted networks. Firstly, FT stability and quasi-stability theorems of dynamical system are discussed, and the results show that the maximum convergence time of FT quasi-stability is smaller than that of FT stability for the dynamic system. Secondly, novel sufficient criteria are gained for FT intra-/inter-layer quasi-synchronization of two-layer multi-weighted networks. Thirdly, the relationship among multiple weights number, the topological structure, inner coupling modes, coupling strengthes and across layers are established. In particular, the results show that the smaller multiple weights number do not necessarily lead to faster quasi-synchronization, and the multiple weights number may have a positive feedback effect on FT intra-/inter-layer quasi-synchronization. When the multiple weights number is greater than a certain value, FT intra-layer quasi-synchronization and FT inter-layer quasi-synchronization of networks can be realized simultaneously, and the conditions of taking the minimum convergence time are also given. Finally, numerical examples verify the effectiveness of the proposed method.