Bifurcations of limit cycles forming compound eyes in the cubic system
type: Item
instance of: scholarly article
title: Bifurcations of limit cycles forming compound eyes in the cubic system
zbMATH Open document ID: 0658.34020
author: Qiming Huang
author: Jibin Li
published in: Chinese Annals of Mathematics. Series B
publication date: 1987-01-01T00:00:00Z
review text: Let H(n) be the maximal number of limit cycle of a planar real polynomial differential system of degree n and \(C^ k_ m\) denote the nest of k limit cycles enclosing m singular points. By computing detection functions, the authors study bifurcation and phase diagrams in the class of a planar cubic disturbed Hamiltonian system. In particular, the following conclusion is reached: The planar cubic system \((E_ 3)\) has 11 limit cycles, which form the pattern of compound eyes of \(C^ 1_ 9\supset 2[C'_ 3\supset (2C^ 2_ 1)]\) and have the symmetrical structure; so the Hilbert number H(3)\(\geq 11\).
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 4075560
zbMATH Keywords: maximal number of limit cycle
zbMATH Keywords: bifurcation
zbMATH Keywords: phase diagrams
zbMATH Keywords: planar cubic disturbed Hamiltonian system
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4075560