Abstract
In this paper, quaternion-valued fuzzy cellular neural networks (QVFCNNs) with time-varying delays are considered. First, we decompose QVFCNNs into their equivalent real-valued systems according to Hamilton’s multiplication rules. Then, we establish the existence and global exponential stability of periodic solutions of QVFCNNs by using the Schauder fixed point theorem and by constructing an appropriate Lyapunov function. Our results are completely new and supplementary to the known results. Finally, we give a numerical example to illustrate the effectiveness of our results.
Highlights
Quaternion was invented by the Irish mathematician W
As far as we know, no scholars have studied the periodic solutions of quaternion-valued fuzzy cellular neural networks (QVFCNNs)
Our main purpose of this paper is by using the Schauder fixed point theorem and constructing an appropriate Lyapunov function to study the existence, the uniqueness, and the global exponential stability of periodic solutions of (1)
Summary
Quaternion was invented by the Irish mathematician W. As far as we know, no scholars have studied the periodic solutions of quaternion-valued fuzzy cellular neural networks (QVFCNNs). Our main purpose of this paper is by using the Schauder fixed point theorem and constructing an appropriate Lyapunov function to study the existence, the uniqueness, and the global exponential stability of periodic solutions of (1). Μq = sup μRq (t) , μIq(t) , μJq(t) , μKq (t) , t∈R
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