Complex dynamics in generalized Hénon map
type: Item
instance of: scholarly article
title: Complex dynamics in generalized Hénon map
zbMATH Open document ID: 1418.37061
DOI: 10.1155/2015/270604
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: The complex dynamics of generalized Hénon map with nonconstant Jacobian determinant are investigated. The conditions of existence for fold bifurcation, flip bifurcation, and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations. Chaos in the sense of Marotto's definition is proved by analytical and numerical methods. The numerical simulations show the consistence with the theoretical analysis and reveal some new complex phenomena which can not be given by theoretical analysis, such as the invariant cycles which are irregular closed graphics, the six and forty-one coexisting invariant cycles, and the two, six, seven, nine, ten, and thirteen coexisting chaotic attractors, and some kinds of strange chaotic attractors.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 7025288
author: Mei-xiang Cai
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/270604
OpenAlex ID: W1999025120
Wikidata QID: Q59105748
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description: scientific article; zbMATH DE number 7025288