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This article discusses the fixed‐time stabilization (FxTS) problem for reaction‐diffusion systems (RDSs). First, this article designs a fixed‐time event‐dependent intermittent control strategy by introducing four nonlinear functions. The switching of the controller between the working and resting phases is no longer time‐dependent, avoiding the relatively stringent constraint on the control ratio in the existing studies of FxTS based on discontinuous‐time control. Under the presented event‐dependent intermittent control strategy, RDSs can be stabilized within a fixed time and the settling time can be estimated as the zero point of the pre‐defined nonlinear function. In contrast to the existing estimation methods, the estimation method of this article is more universal and less conservative. Moreover, this article derives several generalized stabilization criteria for RDSs under event‐dependent intermittent control employing the Lyapunov method and mathematical induction. Finally, an example is given to clarify the validity of the fixed‐time control strategy and the FxTS criteria. [ABSTRACT FROM AUTHOR]

Achieving the robust fixed‐time stabilization (FxTS) of uncertain reaction‐diffusion systems (RDSs) utilizing intermittent boundary control is a valuable and unresolved problem. This paper simultaneously considers the influence of the uncertainty of non‐diffusion and diffusion coefficients on RDSs and provides an effective solution for the treatment of the uncertainty of diffusion coefficient in the investigation of FxTS. Then, a fixed‐time control scheme is presented to stabilize uncertain RDSs within a fixed time, which incorporates the merits of intermittent and boundary control and reduces control costs in both the spatial and temporal domains. Besides, some sufficient conditions in the form of linear matrix inequalities are deduced to guarantee the robust FxTS of uncertain RDSs with Neumann and mixed boundary conditions, respectively, which contain and generalize some existing results. Finally, the validity of the intermittent boundary control scheme and the FxTS criteria developed in this paper are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings. [ABSTRACT FROM AUTHOR]