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This paper mainly considers the fixed-time synchronization (FxTS) and fixed-time anti-synchronization (FxTAS) of discontinuous competitive neural networks with time scales (DCNNTS) modeled by singularly perturbed Filippov system. Different from the previous FxTS results on the competitive networks, new fixed-time stability lemmas with economical inequality conditions are given, which have more relaxed conditions. Then, by means of the established fixed-time stability lemmas and differential inclusions theory, the FxTS and FxTAS of the addressed drive-response DCNNTS are investigated by constructing two different Lyapunov functions and via new designed non-chattering controllers. Notably, the FxTAS of competitive networks is discussed for the first time. Moreover, time-scales-dependent settling times have also been obtained, which further show the effects of time scales on the FxTS and the FxTAS of DCNNTS. Finally, examples and numerical simulations help examine the correctness of the main results.

Based on the framework of Filippov solutions, this paper considers synchronization of inertial neural networks (INNs) with discontinuous activation functions and proportional delay. By designing several non-chattering controllers, both finite-time and fixed-time synchronization are studied. The designed controllers are simple to be implemented and can overcome the effects of both nonidentical uncertainties of Filippov solutions and the proportional delay without inducing any chattering. By designing new Lyapunov functionals and utilizing 1-norm methods, several sufficient conditions are obtained to ensure that the INNs achieve drive-response synchronization in finite time and fixed time, respectively. Moreover, the settling time is estimated for the two types of synchronization. Simulations are provided to illustrate the effectiveness of theoretical analysis.

This paper focuses on the fixed-time synchronization control methodology for a class of delayed memristor-based recurrent neural networks. Based on Lyapunov functionals, analytical techniques, and together with novel control algorithms, sufficient conditions are established to achieve fixed-time synchronization of the master and slave memristive systems. Moreover, the settling time of fixed-time synchronization is estimated, which can be adjusted to desired values regardless of the initial conditions. Finally, the corresponding simulation results are included to show the effectiveness of the proposed methodology derived in this paper.

This paper proposes a novel lemma to study the fixed-time synchronization in probability, which is less conservative and its estimated time is independent of the system’s initial values. Based on the new lemma, the fixed-time synchronization in probability of stochastic drive-response system with discontinuous nodes is investigated by designing a universal and simple controller. As two special cases, two kinds of convenient controllers are designed to realize the fixed-time synchronization in probability of the continuous dynamical system with noise disturbances and the fixed-time synchronization of discontinuous networks. Finally, numerical simulations illustrate the correctness of our main results. Particular, it is found that the gap between the estimated settling time and the real synchronization time can be bridged if the parameters and the index in controllers increase.

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.

In this paper, an improved fixed-time dynamic event-triggered control scheme is developed for solving the synchronization problem of Kuramoto-oscillator network models with and without a pacemaker. First, a set of multiplex control strategies are designed to achieve the phase agreement for Kuramoto networks connected to a pacemaker. Then, the developed strategies are employed to address the phase agreement and frequency synchronization of Kuramoto networks without a pacemaker. For the triggering function, a dynamic variable is introduced to filter out massive unnecessary triggering instants, which significantly reduces the update frequency of the controllers. Moreover, through theoretical analysis, the fixed-time synchronization is guaranteed when the initial phase of nodes are unknown and the coupling strength between nodes are weak. It is also proved that there is no Zeno behavior in the network control dynamics. Finally, three numerical simulation experiments are given to demonstrate the validity of the proposed dynamic event-triggered control scheme.

In this article, sufficient conditions for fixed-time synchronization of time-delayed quaternion-valued neural networks (QVNNs) are derived. Firstly, QVNNs are decomposed into four real-valued systems. Then using the available lemmas and by constructing the Lyapunov function, the synchronization criterion for the neural networks is proposed. Activation functions satisfy the Lipschitz condition. A suitable controller has been designed to synchronize the master–slave systems. The effectiveness of the proposed result is validated through a comparison of the settling time obtained by applying two different existing lemmas to a particular problem of synchronization of two identical QVNNs with time-varying delay with the help of suitable controllers.

This study addresses the problem of fast fixed-time synchronization (FDTS) in multi-layer networks (MLNs), focusing on both intra-layer and inter-layer dynamic synchronization. First, we propose a more representative MLN framework in which each layer has a distinct topological structure, and node-to-node connections are established between corresponding nodes across layers. Second, we design a fast fixed-time controller to achieve synchronization of MLNs and estimate the synchronization time. Third, by applying the Lyapunov method and comparison theorem, we derive several novel synchronization conditions that are independent of initial states. Finally, numerical simulations are conducted to validate the theoretical findings.

This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results.

This paper is devoted to studying the finite-time and fixed-time of inertial Cohen–Grossberg type neural networks (ICGNNs) with time varying delays. First, by constructing a proper variable substitution, the original (ICGNNs) can be rewritten as first-order differential system. Second, by utilizing feedback controllers and constructing suitable Lyapunov functionals, several new sufficient conditions guaranteeing the finite-time and the fixed-time synchronization of ICGNNs with time varying delays are obtained based on different finite-time synchronization analysis techniques. The obtained sufficient conditions are simple and easy to verify. Numerical simulations are given to illustrate the effectiveness of the theoretical results.