$$(\mu ,\nu )-$$Pseudo Almost Automorphic Solutions of Neutral Type Clifford-Valued High-Order Hopfield Neural Networks with D Operator

Abstract

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Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays

“…Consequently, the research of Clifford-valued neural networks has become a research hotspot in recent years. Nevertheless, there are few results on the dynamics of Clifford-valued neural networks [17][18][19][20][21][22][23][24]. In addition, many existing results are obtained by decomposing Clifford-valued neural networks into realvalued neural networks [25][26][27][28][29][30][31][32], which brings some difficulties to the direct application of these results.…”

“…It is widely known that recurrent oscillation is an important dynamics of non-autonomous neural networks. Therefore, in the past few decades, many scholars have studied the periodic oscillation, anti-periodic oscillation, almost periodic oscillation and almost automorphic oscillation of neural networks [19][20][21][22][33][34][35][36]. Almost automorphy is a natural extension of almost periodicity.…”

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].…”

Pseudo compact almost automorphy of neutral type Clifford-valued neural networks with mixed delays

“…for ordinary differential equations, functional differential equations and abstract evolutionary equations has been widely studied [4][5][6][7]. Of course, similar to the case of almost periodic functions, since the concept of almost automorphic functions was introduced into mathematics, its varieties and generalizations have been proposed and studied, such as asymptotically almost automorphy, pseudo almost automorphy, weighted pseudo almost automorphy and so on.…”