Fixed/preassigned-time bipartite synchronization for delayed fractional-order multilayer multi-link signed networks via adaptive aperiodically semi-intermittent control

Abstract

In this paper, the bipartite synchronization (BS) problem of fractional-order multilayer multi-link signed networks (FOMMKSNs) with internal time-varying delay, intra-layer and inter-layer coupling time-varying delays is studied in fixed-time or preassigned-time. Firstly, a mathematical model is established by integrating the fractional-order dynamics of nodes, the edges of multilayer and multi-link networks, and the positive and negative weights, making it more diverse and practical. Secondly, an expanded fixed-time aperiodically intermittent strategy theory is proposed, building on the existing theory, along with an improved estimation of the settling time (ST). Then, utilizing the signed graph theory and Lyapunov method, several sufficient conditions for fixed-time BS (FXTBS) of FOMMKSNs are derived through an adaptive aperiodically semi-intermittent control scheme. Furthermore, based on the FXTBS results, a new controller is designed to study the BS of FOMMKSNs within a specified time, where the ST is independent of any initial values and parameters of the network and the controller. Finally, the effectiveness of the obtained results is verified by two simulation examples.