Global Asymptotic Almost Periodic Synchronization of Clifford‐Valued CNNs with Discrete Delays

Abstract

In this paper, we are concerned with Clifford-valued cellular neural networks (CNNs) with discrete delays. Since Clifford algebra is a unital associative algebra and its multiplication is noncommutative, to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers, we first decompose the considered Clifford-valued neural network into 2m2n real-valued systems. Second, based on the Banach fixed point theorem, we establish the existence and uniqueness of almost periodic solutions of the considered neural networks. Then, by designing a novel state-feedback controller and constructing a proper Lyapunov function, we study the global asymptotic synchronization of the considered neural networks. Finally, a numerical example is presented to show the effectiveness and feasibility of our results.

Dynamics behavior for second-order neutral Clifford differential equations: inertial neural networks with mixed delays

“…(b) The inclusion of different types of delay: infinite distributed delay and time-varying delay. We generalize the results of the papers (Liu et al 2016;Li and Xiang 2019;. (c) In our system, we not only consider the effects of mixed delays on Clifford-valued neural networks, but also the influences of neutral terms on the networks.…”

“…It is well known that p.a.p solutions are more general and complicated than periodic and a.p solutions (Aouiti et al 2019a). Recently, in Li and Xiang (2019), the authors investigated the global asymptotic a.p synchronisation of Clifford-valued NNs with delay by using Banach fixed point theorem and Lyapunov function. The authors in studied the existence and global exponential stability of p.a.p solution for Clifford-valued neutral high-Order Hopfield NNs with leakage delays.…”

“…The authors in studied the existence and global exponential stability of p.a.p solution for Clifford-valued neutral high-Order Hopfield NNs with leakage delays. Note that, in Li and Xiang (2019), authors studied the dynamics behaviours of NNs with only first-order states, while it is also of significant importance to added an inertial term, because in inertial NNs system, the inertia can be considered a useful tool, which have a great impact in the dynamics behaviours of NNs, and has a very important role in the generation of chaos Aouiti et al (2019b). For instance, the authors in Li et al (2004) added the inertia term to differential equation with delay which can be described by the following equations:…”

Existence and Global Exponential Stability of Almost Automorphic Solution for Clifford‐Valued High‐Order Hopfield Neural Networks with Leakage Delays

“…Therefore, the current results on the dynamics of Clifford-valued neural networks are still very rare. At present, only a few papers have been published on the dynamics of Clifford-valued neural networks [18][19][20][21][22]. It is worth mentioning that the results of these mentioned papers are obtained by decomposing Clifford-valued neural networks into real-valued networks.…”

Pseudo-almost-periodic solutions of quaternion-valued RNNs with mixed delays via a direct method

“…Recurrence oscillation of neural networks is an important dynamic behavior of neural networks, such as periodic oscillation, almost periodic oscillation, almost automorphic oscillation, and so on. Many scholars have studied these oscillation problems of neural networks [16][17][18][19][20][21]. The pseudo-almostperiodic functions as a generalization of almost periodic functions were introduced into the research field of mathematics by Zhang [22].…”