Finite-time Mittag-Leffler synchronization of delayed fractional-order discrete-time complex-valued genetic regulatory networks: Decomposition and direct approaches

The complex-valued molecular model of mRNA and protein plays a crucial role in the regulatory mechanisms governing gene expression in the genetic regulatory network (GRN). In this study, we introduced a novel GRN utilizing the fractional-order discrete-time complex-valued molecular model of mRNA and protein. Both decomposition and a direct approach are employed to investigate the nonlinear regulatory function within complex-valued molecular models. New conditions are established to ensure the finite-time Mittag-Leffler synchronization (FTMLS) of the error model dynamics. Feedback controllers are applied to derive the FTMLS conditions for delayed fractional-order discrete-time complex-valued genetic regulatory networks (DFDTCVGRNs). By applying the first-order backward difference on the Lyapunov functional under the definition of fractional Caputo difference and fractional calculus theory, sufficient conditions are derived. Finally, two numerical examples are provided to illustrate the FTMLS criteria obtained.