Finite-Time Synchronization of Fractional-Order Complex-Variable Dynamic Networks

In this paper, without dividing complex-variable networks into two subsystems with real values, the finite-time synchronization is considered for complex-valued dynamical networks with fractional order by means of the theory of complex-variable functions. First of all, as a generalization of the real-valued sign function, the sign functions of complex-valued numbers and complex-valued vectors are introduced and some formulas about them are established. Under the sign function framework, two complex-valued control strategies are designed based on two different norms of complex numbers. Some synchronization criteria are derived and the settling times of synchronization are effectively estimated by developing fractional-order finite-time differential inequalities and utilizing the theory of complex-variable functions. The established theoretical results are demonstrated and the effect of the fractional order of the network model on the finite-time synchronization is revealed finally by providing some numerical simulations.

Automated summary

In this paper, finite-time synchronization of complex-valued dynamical networks with fractional order is considered without dividing networks into two subsystems, using the theory of complex-variable functions. Sign functions for complex-valued numbers and vectors were introduced, along with two complex-valued control strategies based on different norms of complex numbers. Synchronization criteria were derived and settling times were estimated effectively through fractional-order finite-time differential inequalities and the theory of complex-variable functions. Numerical simulations were provided to demonstrate the established theoretical results and the impact of fractional order on finite-time synchronization.