Besicovitch Almost Anti-periodic Solution of Octonion-Valued Cohen–Grossberg Neural Networks with Delays on Time Scales

Abstract

In this work, we put forward a concept of Besicovitch almost anti-periodic functions on time scales, which is new even when time scale T=R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {T}=\\mathbb {R}$$\\end{document} or Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}$$\\end{document}. Based on this, we use the fixed point theorem and analytical techniques to obtain the existence, uniqueness and global exponential stability of Besicovitch almost anti-periodic solutions for a class of octonion-valued Cohen–Grossberg neural networks with time delays on time scales. Finally, the validity of the results is verified by a numerical example.