Global Synchronization and Anti-Synchronization of Fractional-Order Complex-Valued Gene Regulatory Networks With Time-Varying Delays

Abstract

This paper presents the analytical and numerical investigation on the global synchronization and anti-synchronization for a class of drive-response systems of fractional-order complex-valued gene regulatory networks with time-varying delays (DFGRNs). In our design, two kinds of adaptive feedback controllers are used to synchronize and anti-synchronize the proposed drive-response systems, and some sufficient conditions on the global asymptotical synchronization and anti-synchronization are given with the methods of the fractional Lyapunov-like functions and the fractional-order inequalities. In the numerical simulations, two minimum “estimated time”, T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , are computed to achieve the synchronization and anti-synchronization. We find that T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> increase with the decreasing of the fractional order of DFGRNs.