Quasi-synchronization for variable-order fractional complex dynamical networks with hybrid delay-dependent impulses.

Abstract

This paper focuses on addressing the problem of quasi-synchronization in heterogeneous variable-order fractional complex dynamical networks (VFCDNs) with hybrid delay-dependent impulses. Firstly, a mathematics model of VFCDNs with short memory is established under multi-weighted networks and mismatched parameters, which is more diverse and practical. Secondly, under the framework of variable-order fractional derivative, a novel fractional differential inequality has been proposed to handle the issue of quasi-synchronization with hybrid delay-dependent impulses. Additionally, the quasi-synchronization criterion for VFCDNs is developed using differential inclusion theory and Lyapunov method. Finally, the practicality and feasibility of this theoretical analysis are demonstrated through numerical examples.