Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method

Abstract

The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts’ absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation.

Adaptive Control for Finite-Time Cluster Synchronization of Fractional-Order Fully Complex-Valued Dynamical Networks

“…It is not difficult to verify that many chaotic dynamical systems satisfy Assumption 2, such as the Lorenz system, the Chua system, delayed DNs, etc. [33][34][35].…”

“…Remark 6. In recent years, scholars have conducted research on the finite-time synchronization problem of FCVDNs [17,25,30,33]. However, there are some limitations in these studies, as listed below.…”

“…Secondly, time delay was not considered in [17,25,30], which is a common phenomenon in reality. Thirdly, when using state feedback control in [33], the feedback strength is fixed, which is less energy-efficient compared to the adaptive control strategy used in this paper. Remark 7.…”