Pseudo almost periodic synchronization of Clifford-valued fuzzy cellular neural networks with time-varying delays on time scales

Abstract

At present, the research on discrete-time Clifford-valued neural networks is rarely reported. However, the discrete-time neural networks are an important part of the neural network theory. Because the time scale theory can unify the study of discrete- and continuous-time problems, it is not necessary to separately study continuous- and discrete-time systems. Therefore, to simultaneously study the pseudo almost periodic oscillation and synchronization of continuous- and discrete-time Clifford-valued neural networks, in this paper, we consider a class of Clifford-valued fuzzy cellular neural networks on time scales. Based on the theory of calculus on time scales and the contraction fixed point theorem, we first establish the existence of pseudo almost periodic solutions of neural networks. Then, under the condition that the considered network has pseudo almost periodic solutions, by designing a novel state-feedback controller and using reduction to absurdity, we obtain that the drive-response structure of Clifford-valued fuzzy cellular neural networks on time scales with pseudo almost periodic coefficients can realize the global exponential synchronization. Finally, we give a numerical example to illustrate the feasibility of our results.

Finite/fixed-time synchronization control of fuzzy inertial cellular neural networks with mixed delays

“…Until now, FCNN is still a hot topic. Many researchers have revealed that FCNN has a wide range of applications in the field of intelligent computing(see Cui et al, 2021; Duan et al, 2019a; Li and Shen, 2020b; Wang, 2018). Therefore, studying the dynamical behavior of FCNN has important theoretical and practical significance.…”

Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method

“…The usual ways of studying the stability of RVNN and CVNN cannot be directly applied to research the same issues of QNN. To overcome the challenge, decomposition approaches are proposed, which splits the considered QVNN into equivalent four RVNNs or two CVNNs [11][12][13][14][15][16][17][18]. However, the decomposition methods have observable limitations: (i) they require the activation functions to be decomposable; yet, not all quaternion functions are decomposable; (ii) the decomposition methods often induce a bulky computing cost.…”

Existence and Global Attractivity of Pseudo Almost Periodic Solutions for Clifford-Valued Fuzzy Neural Networks with Proportional Delays

“…The Clifford-valued neural network is a generalization of a real-valued neural network, complex-valued neural network, and quaternion-valued neural network, and has been shown superior to a real-valued neural network [1,2]. Because the multiplication of Clifford algebra does not meet the commutative law, there are few results on the dynamics of Clifford-valued neural networks [3][4][5][6][7][8][9][10][11]. Many existing results are obtained by decomposing a Clifford-valued system into a real-value system [3][4][5][6].…”

“…Many existing results are obtained by decomposing a Clifford-valued system into a real-value system [3][4][5][6]. Therefore, it is a meaningful and challenging work to study the dynamics of Clifford-valued systems via a direct method; that is, without decomposing Clifford-valued systems into real-valued systems [7][8][9][10][11].…”