Abstract
In this paper, we study the existence of weighted pseudo-almost periodic solutions and the global exponential synchronization of delayed quaternion-valued cellular neural networks (QVCNNs). Firstly, we use the Banach fixed point theorem to establish the existence of weighted pseudo-almost periodic solutions for this class of QVCNNs. Then, under the condition that the drive system has a unique weighted pseudo-almost periodic solution, by designing a state-feedback controller and constructing suitable Lyapunov functions, we see that the drive–response structure of delayed QVCNNs with weighted pseudo-almost periodic coefficients achieve global exponential synchronization. Finally, a numerical example is given to illustrate the feasibility of our results.
Highlights
1 Introduction Cellular neural networks (CNNs), which were originally proposed by Chua and Yang in [1, 2], have been widely used in signal processing, pattern recognition, associative memory, combinatorial optimization, intelligent robot control, and other new fields of application are constantly being discovered
6 Conclusion In this work, we studied the existence of weighted pseudo-almost periodic solutions of delayed quaternion-valued cellular neural networks (QVCNNs)
The approach of this paper can be used to study the problem of the weighted pseudo-almost periodic solutions and synchronization for other types of neural networks
Summary
Cellular neural networks (CNNs), which were originally proposed by Chua and Yang in [1, 2], have been widely used in signal processing, pattern recognition, associative memory, combinatorial optimization, intelligent robot control, and other new fields of application are constantly being discovered. The collection of all weighted pseudo-almost periodic functions f : R → Rn will be denoted by PAP(R, Rn, ν). Throughout the paper, we assume that the following conditions hold: (H1) For p, q ∈ S, cp ∈ C(R, R+) with c–p = inft∈R cp(t) > 0, apq, bpq ∈ PAP(R, H, μ), τpq ∈ AP(R, R+), for fixed ν ∈ WI∞nv, and Jp ∈ PAP(R, H).
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