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This paper discusses finite/fixed-time (FNT/FXT) synchronization of multi-layer networks based on energy consumption estimation. Firstly, a novel FXT stability theorem of dynamical system is presented. Secondly, sufficient criteria for FNT/FXT synchronization in multi-layer networks are given, and the estimation of the energy consumption are also gained. Especially, the range of the number of layers of network is gained based on the least convergence time and the estimation of the least energy consumption. The results show that shorter synchronization time and less energy consumption does not mean less network layers. Finally, the validity of the theoretical method is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]