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Zero‐zero‐Hopf bifurcation and ultimate bound estimation of a generalized Lorenz–Stenflo hyperchaotic system
Author(s) -
Chen YuMing,
Liang HaiHua
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4236
Subject(s) - mathematics , zero (linguistics) , bifurcation , eigenvalues and eigenvectors , hopf bifurcation , mathematical analysis , dynamics (music) , nonlinear system , physics , philosophy , linguistics , quantum mechanics , acoustics
This paper is devoted to the analysis of complex dynamics of a generalized Lorenz–Stenflo hyperchaotic system. First, on the local dynamics, the bifurcation of periodic solutions at the zero‐zero‐Hopf equilibrium (that is, an isolated equilibrium with double zero eigenvalues and a pair of purely imaginary eigenvalues) of this hyperchaotic system is investigated, and the sufficient conditions, which insure that two periodic solutions will bifurcate from the bifurcation point, are obtained. Furthermore, on the global dynamics, the explicit ultimate bound sets of this hyperchaotic system are obtained. Copyright © 2016 John Wiley & Sons, Ltd.