Synchronization of complex-valued neural networks with mixed two additive time-varying delays

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.

Prespecified-time synchronization of switched coupled neural networks via smooth controllers

This paper considers the prespecified-time synchronization issue of switched coupled neural networks (SCNNs) under some smooth controllers. Different from the traditional finite-time synchronization (FTS), the synchronization time obtained in this paper is independent of control gains, initial values or network topology, which can be pre-set as to the task requirements. Moreover, unlike the existing nonsmooth or even discontinuous FTS control strategies, the new proposed control protocols are fully smooth, which abandon the common fractional power feedbacks or signum functions. Finally, two illustrative examples are provided to illustrate the effectiveness of the theoretical results.

Exponential and adaptive synchronization of inertial complex-valued neural networks: A non-reduced order and non-separation approach

This paper mainly deals with the problem of exponential and adaptive synchronization for a type of inertial complex-valued neural networks via directly constructing Lyapunov functionals without utilizing standard reduced-order transformation for inertial neural systems and common separation approach for complex-valued systems. At first, a complex-valued feedback control scheme is designed and a nontrivial Lyapunov functional, composed of the complex-valued state variables and their derivatives, is proposed to analyze exponential synchronization. Some criteria involving multi-parameters are derived and a feasible method is provided to determine these parameters so as to clearly show how to choose control gains in practice. In addition, an adaptive control strategy in complex domain is developed to adjust control gains and asymptotic synchronization is ensured by applying the method of undeterminated coefficients in the construction of Lyapunov functional and utilizing Barbalat Lemma. Lastly, a numerical example along with simulation results is provided to support the theoretical work.