This paper addresses the problem of Mittag-Leffler synchronization of T–S fuzzy fractional-order discrete-time complex-valued molecular models of mRNA and protein in regulatory mechanisms with two kinds of regulation functions, respectively. A novel approach is proposed to effectively deal with the joint effects from leakage delay and time varying delay for the class of T–S fuzzy fractional-order discrete-time complex-valued genetic regulatory networks (FDTCVGRNs). By employing Lyapunov stability method and Caputo fractional difference inequalities, several effective conditions according to algebraic inequality and complex-valued linear matrix inequalities are deduced to guarantee the synchronization of the addressed FDTCVGRNs. Moreover, Mittag-Leffler synchronization problem of the nonlinear regulation function in complex-valued molecular models on the basis of general regulation function and linear threshold one. Compared with existing results in the literature, our results are less conservative than existing ones. Finally, simulation results with two numerical examples are demonstrated, which proves the validity of the proposed method.

本文解决了分别具有两种调节功能的调节机制中mRNA和蛋白质的T-S模糊分数阶离散时间复值分子模型的Mittag-Leffler同步问题。提出了一种新方法来有效处理 T-S 模糊分数阶离散时间复值遗传调控网络 (FDTCVGRNs) 类的泄漏延迟和时变延迟的联合效应。利用Lyapunov稳定性方法和Caputo分数差分不等式，根据代数不等式和复值线性矩阵不等式推导了几个有效条件，以保证所解决的FDTCVGRN的同步。而且，基于一般调节函数和线性阈值一的复值分子模型中非线性调节函数的Mittag-Leffler同步问题。与文献中的现有结果相比，我们的结果不如现有结果保守。最后，通过两个数值例子验证了仿真结果，证明了所提方法的有效性。