Finite-time synchronization of complex-valued neural networks with finite-time distributed delays

Fixed-time synchronization for two-dimensional coupled reaction-diffusion complex networks: Boundary conditions analysis

This paper examines fixed-time synchronization (FxTS) for two-dimensional coupled reaction-diffusion complex networks (CRDCNs) with impulses and delay. Utilizing the Lyapunov method, a FxTS criterion is established for impulsive delayed CRDCNs. Herein, impulses encompass both synchronizing and desynchronizing variants. Subsequently, by employing a Lyapunov-Krasovskii functional, two FxTS boundary controllers are formulated for CRDCNs with Neumann and mixed boundary condition, respectively. It is observed that vanishing Dirichlet boundary contributes to the synchronization of the CRDCNs. Furthermore, this study calculates the optimal constant for the Poincaré inequality in the square domain, which is instrumental in analyzing FxTS conditions for boundary controllers. Conclusive numerical examples underscore the efficacy of the proposed theoretical findings.

Synchronization of inertial complex-valued memristor-based neural networks with time-varying delays

The synchronization of inertial complex-valued memristor-based neural networks (ICVMNNs) with time-varying delays was explored in the paper with the non-separation and non-reduced approach. Sufficient conditions required for the exponential synchronization of the ICVMNNs were identified with the construction of comprehensive Lyapunov functions and the design of a novel control scheme. The adaptive synchronization was also investigated based on the derived results, which is easier to implement in practice. What's more, a numerical example that verifies the obtained results was presented.

Exponential Synchronization of Inertial Complex-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays via Periodically Intermittent Control

This paper mainly studies the exponential synchronization issue for the inertial complex-valued fuzzy cellular neural networks (ICVFCNNs) with time-varying delays via periodically intermittent control. To achieve exponential synchronization, we use a non-reduced order and non-separation approach, which is a supplement and innovation to the previous method. Based on directly constructing Lyapunov functional and a novel periodically intermittent control scheme, sufficient conditions for achieving the exponential synchronization of the ICVFCNNs are established. Finally, an example is given to illustrate the validity of the obtained results.

Pinning synchronization control for stochastic multi-layer networks with coupling disturbance

The pinning synchronization scheme is investigated for stochastic multi-layer networks under the intra-layer coupling disturbance and stochastic noise. To save the control cost, a pinning control scheme is proposed. And some sufficient conditions in the form of the LMI are given, based on Lyapunov theory and stochastic analysis, to make sure that the multi-layer networks synchronize to a desired trajectory. Next, the selection scheme of pinned nodes is designed according to the structure of considered multi-layer networks. Finally, simulation examples are shown to illustrate the feasibility and availability of the designed pinning scheme.

Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays

In this paper, we explore the finite-time synchronization of Clifford-valued neural networks with finite-time distributed delays. To address the problem associated with non-commutativity pertaining to the multiplication of Clifford numbers, the original n-dimensional Clifford-valued drive and response systems are firstly decomposed into the corresponding 2m-dimensional real-valued counterparts. On the basis of a new Lyapunov–Krasovskii functional, suitable controller and new computational techniques, finite-time synchronization criteria are formulated for the corresponding real-valued drive and response systems. The feasibility of the main results is verified by a numerical example.

Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional

In this paper we consider a standard class of the neural networks and propose an investigation of the global asymptotic stability of these neural systems. The main aim of this investigation is to define a novel Lyapunov functional having quadratic-integral form and use it to reach a stability criterion for the under study neural networks. Since some fundamental characteristics, such as nonlinearity, including time-delays and neutrality, help us design a more realistic and applicable model of neural systems, we will use all of these factors in our neural dynamical systems. At the end, some numerical simulations are presented to illustrate the obtained stability criterion and show the essential role of the time-delays in appearance of the oscillations and stability in the neural networks.