Abstract
In this paper, we consider the existence and global exponential stability of pseudo almost automorphic solutions to quaternion-valued cellular neural networks with infinitely distributed delays. Unlike most previous studies of quaternion-valued cellular neural networks, we do not decompose the systems under consideration into real-valued or complex-valued systems, but rather directly study quaternion-valued systems. Our method and the results of this paper are new. An example is given to show the feasibility of our main results.
Highlights
1 Introduction The quaternion was introduced into mathematics in 1843 by Hamilton [1]
The main purpose of this paper is to study the existence and global exponential stability of pseudo almost automorphic solutions to system [1]
We prove that φp ∈ PAA(R, H)
Summary
The quaternion was introduced into mathematics in 1843 by Hamilton [1]. The skew field of quaternions isH := q|q = qR + iqI + jqJ + kqK , where qR, qI, qJ , qK ∈ R and i, j, k satisfy Hamilton’s multiplication table formed by i2 = j2 = k2 = ijk = –1, ij = –ji = k, jk = –kj = i, ki = –ik = j, and the norm of q ∈ H is q H = qq = qq = qR 2 + qI 2 + qJ 2 + qK 2, where q = qR – iqI – jqJ – kqK. The quaternion was introduced into mathematics in 1843 by Hamilton [1]. H := q|q = qR + iqI + jqJ + kqK , where qR, qI, qJ , qK ∈ R and i, j, k satisfy Hamilton’s multiplication table formed by i2 = j2 = k2 = ijk = –1, ij = –ji = k, jk = –kj = i, ki = –ik = j, and the norm of q ∈ H is q H = qq = qq = qR 2 + qI 2 + qJ 2 + qK 2, where q = qR – iqI – jqJ – kqK. H. Quaternion algebra is a non-commutative divisible algebra. Quaternion algebra is a non-commutative divisible algebra It is because of its non-commutative nature that the study of quaternions is much more difficult than real and complex numbers. With the rapid development of quaternion algebra and the wide application of quaternions in many fields, the
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