Four-dimensional Zero-Hopf Bifurcation of Quadratic Polynomial Differential System, via Averaging Theory of Third Order

摘要

This article concerns the zero-Hopf bifurcation of a quadratic polynomial differential system in ℝ4documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$mathbb {R}^{4}$end{document}. By using the averaging theory of third order, we provide that at most 25 limit cycles can bifurcate from one singularity with eigenvalues of the form ± bi, 0 and 0.