Article Contents
Article Contents

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

• * Corresponding author: Yongkun Li

The first author is supported by the National Natural Science Foundation of China under Grant No. 11861072 and the second author is supported by the Applied Basic Research Foundation of Yunnan Province under Grant No. 2019FB003

• We consider a class of neutral type Clifford-valued cellular neural networks with discrete delays and infinitely distributed delays. Unlike most previous studies on Clifford-valued neural networks, we assume that the self feedback connection weights of the networks are Clifford numbers rather than real numbers. In order to study the existence of $(\mu, \nu)$-pseudo compact almost automorphic solutions of the networks, we prove a composition theorem of $(\mu, \nu)$-pseudo compact almost automorphic functions with varying deviating arguments. Based on this composition theorem and the fixed point theorem, we establish the existence and the uniqueness of $(\mu, \nu)$-pseudo compact almost automorphic solutions of the networks. Then, we investigate the global exponential stability of the solution by employing differential inequality techniques. Finally, we give an example to illustrate our theoretical finding. Our results obtained in this paper are completely new, even when the considered networks are degenerated into real-valued, complex-valued or quaternion-valued networks.

Mathematics Subject Classification: Primary: 34K40, 34K14, 34K20; Secondary: 92B20.

 Citation:

• Figure 1.  Curves of $x_{p}^{0}(t)$ and $x_{p}^{1}(t)$ of system (1) with the initial values $(x_{1}^{0}(0), x_{2}^{0}(0))^{T} = (0.05, -0.1)^{T}, (-0.06, 0.09)^{T}$ and $(x_{1}^{1}(0), x_{2}^{1}(0))^{T} = (-0.1, 0.05)^{T}, (0.1, -0.04)^{T}$

Figure 2.  Curves of $x_{p}^{2}(t)$ and $x_{p}^{3}(t)$ of system (1) with the initial values $(x_{1}^{2}(0), x_{2}^{2}(0))^{T} = (-0.03, 0.1)^{T}, (-0.1, 0.02)^{T}$ and $(x_{1}^{3}(0), x_{2}^{3}(0))^{T} = (0.1, -0.1)^{T}, (0.04, -0.02)^{T}$

Figure 3.  Curves of $x_{p}^{12}(t)$ and $x_{p}^{13}(t)$ of system (1) with the initial values $(x_{1}^{12}(0), x_{2}^{12}(0))^{T} = (-0.04, 0.04)^{T}, (0.08, -0.07)^{T}$ and $(x_{1}^{13}(0), x_{2}^{13}(0))^{T} = (0.07, -0.06)^{T}, (-0.02, 0.03)^{T}$

Figure 4.  Curves of $x_{p}^{23}(t)$ and $x_{p}^{123}(t)$ of system (1) with the initial values $(x_{1}^{23}(0), x_{2}^{23}(0))^{T} = (0.08, 0.02)^{T}, (-0.1, -0.04)^{T}$ and $(x_{1}^{123}(0), x_{2}^{123}(0))^{T} = (0.03, -0.02)^{T}, (-0.1, 0.08)^{T}$

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