In this paper, we discussed the fixed-time synchronization of fractional-order memristor-based fuzzy cellular neural networks (FMFCNNs) with time-varying delays. Based on the differential inclusion theory and discontinuous state feedback control technique, some useful novel criteria of the fixed-time synchronization for FMFCNNs are derived by constructing appropriate Lyapunov function. The results in our paper improve and generalize current literature research results significantly. Finally, the effectiveness of our control schemes for the fixed-time synchronization is demonstrated through numerical simulations.

Due to the widespread application of neural networks (NNs), and considering the respective advantages of fractional calculus (FC), inertial neural networks (INNs), cellular neural networks (CNNs), and fuzzy neural networks (FNNs), this paper investigates the fixed-time synchronization (FDTS) issues for a particular category of fractional-order cellular-inertial fuzzy neural networks (FCIFNNs) that involve mixed time-varying delays (MTDs), including both discrete and distributed delays. Firstly, we establish an appropriate transformation variable to reformulate FCIFNNs with MTD into a differential first-order system. Then, utilizing the finite-time stability (FETS) theory and Lyapunov functionals (LFs), we establish some new effective criteria for achieving FDTS of the response system (RS) and drive system (DS). Eventually, we offer two numerical examples to display the effectiveness of our proposed synchronization strategies. Moreover, we also demonstrate the benefits of our approach through an application in image encryption.

This paper mainly investigates the stability analysis and synchronization control of a fractional-order time-varying delay inertial neural network. Firstly, a time-varying delay inertial neural network model is established, which is easy to implement in engineering applications. Secondly, based on the properties of the Caputo fractional derivative and the proposed lemma, the original inertial system is transferred into conventional system through the proper variable substitution, and a synchronous control strategy for the time varying delay inertial network is then established. In addition, the stability conditions of a class of Caputo fractional-order time-delay inertial neural networks are given. Finally, three simulation examples are given to verify the rationality and effectiveness of the method proposed in this paper.

The present paper investigates the fixed-time synchronization for fuzzy cellular neural networks with timevarying delays and discontinuous activations. In the framework of differential inclusions, new and useful fixed-time synchronization criteria for the networks considered are established by utilizing the discontinuous state feedback control and constructing Lyapunov functionals, which significantly generalize and improve recent works in the literature. Numerical simulations are given to show the effectiveness of the fixed-time synchronization schemes.

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

Finite-time synchronization depends on the initial conditions of the system in question. However, the initial conditions of an actual system are often difficult to estimate or even unknown. Therefore, a more valuable and pressing problem is fixed-time synchronization (FTS). This paper addresses the issue of FTS for a specific class of fractional-order memristive fuzzy neural networks (FOMFNNs) that include both leakage and transmission delays. We have designed two distinct discontinuous control methodologies that account for these delays: a state feedback control scheme and a fractional-order adaptive control strategy. Leveraging differential inclusion theory and fractional-order differential inequalities, we derive several novel algebraic conditions that are independent of delay. These conditions ensure the FTS of drive–response FOMFNNs in the presence of leakage and transmission delays. Additionally, we provide an estimate for the upper bound of the settling time required to achieve FTS. Finally, to validate the feasibility and applicability of our theoretical findings, we present two numerical examples which are accompanied by simulations.