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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.

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 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.

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.

Finite-time synchronization is a crucial phenomenon observed in nonlinear complex systems, the settling time in such a dynamic phenomenon is heavily depends on the initial states which may be unaccessible beforehand in the real world. Eliminating the dependence of the settling time on initial states leads to major advantage and convenience in practical applications. This paper is concerned with the fixed-/preassigned-time synchronization of delayed complex-valued neural networks(CVNNs) with discontinuous activations. By designing novel state feedback controllers, and with the help of Filippov regularization and inequality techniques, some new criteria for achieving fixed-/preassigned-time synchronization are established. The obtained theoretical results cover and supplement existing ones of the CVNNs with continuous activations. In addition, the upper-bound of the settling time is explicitly estimated. Finally, the validity of the theoretical results is supported by numerical simulations.

This paper investigates finite-time (FET) and fixed-time (FDT) synchronization of discontinuous complex networks (CNs) via quantized controllers. These control schemes can take full advantage of limited communication resources. By designing Lyapunov function and using different control schemes, several sufficient conditions are proposed such that the dynamical CNs are able to realize synchronization within a settling time. The settling time is related to the initial values of the considered systems using FET control, while it is regardless of the initial values when a special case of FET control named FDT control is utilized. Moreover, FET and FDT synchronization of discontinuous CNs are also considered via some existing controllers without logarithmic quantization, respectively. Numerical simulations are presented to demonstrate the theoretical results.

This paper considers the finite-time and fixed-time synchronization of delayed complex-valued recurrent neural networks (CVRNNs) with discontinuous activation functions and nonidentical parameters via sliding mode control. Firstly, we design a sliding surface involving integral structure and a discontinuous control. Secondly, by constructing Lyapunov functional and using the differential inequality technique, some sufficient conditions are derived to guarantee the finite-time and fixed-time synchronization of delayed complex-valued recurrent neural networks with discontinuous activation functions and nonidentical parameters. Finally, two simulation examples are shown to illustrate the proposed methods.

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 article focuses on the problem of finite-time and fixed-time synchronization for Cohen–Grossberg neural networks (CGNNs) with time-varying delays and memristor connection weights. First, through a nonlinear transformation, an alternative system is derived from the Cohen–Grossberg memristor-based neural networks (MCGNNs) considered. Then, under the framework of the Filippov solution and by adjusting a key control parameter, some novel and effective criteria are obtained to ensure finite-time or fixed-time synchronization of the alternative networks via the unified control framework and under the same conditions. Furthermore, the two types of synchronization criteria are derived from the considered MCGNNs. Finally, some numerical simulations are presented to test the validity of these theoretical conclusions.