Finite-time cluster synchronization in complex-variable networks with fractional-order and nonlinear coupling.

Abstract

This paper is primarily concentrated on finite-time cluster synchronization of fractional-order complex-variable networks with nonlinear coupling by utilizing the non-decomposition method. Firstly, two control strategies are designed which are relevant to complex-valued sign functions. Thereafter, by employing fractional-order stability theory and complex function theory, several criteria are deduced to ensure finite-time cluster synchronization under the framework within a new norm consisting of absolute values for real and imaginary components. Furthermore, the setting time is effectively estimated based on some significant properties of fractional-order Caputo derivation and Mittag-Leffler functions. Lastly, two numerical examples are given to verify the effectiveness of theoretical results.