A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family

In this paper, we give a constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family, which contains four independent parameters and is more general than any Lorenz systems studied so far in the literature. The system considered in...

Full description

Saved in:
Bibliographic Details
Published inCommunications in nonlinear science & numerical simulation Vol. 14; no. 7; pp. 2886 - 2896
Main Authors Yu, P., Liao, X.X., Xie, S.L., Fu, Y.L.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2009
Subjects
Computer simulation
Construction
General Lorenz family
Generalized Lyapunov function
Globally exponentially attractive set
Invariants
Lorenz system
Mathematical models
Nonlinearity
Positive invariant set
Proving
Ultimate boundedness of chaotic system
General Lorenz family
Positive invariant set
02.30.Hq
Generalized Lyapunov function
Globally exponentially attractive set
Ultimate boundedness of chaotic system
Online AccessGet full text

Cover

More Information
Summary:In this paper, we give a constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family, which contains four independent parameters and is more general than any Lorenz systems studied so far in the literature. The system considered in this paper not only contains the classical Lorenz system and the generalized Lorenz family as special cases, but also provides three new Lorenz systems, which do not belong to the generalized Lorenz system, but the general Lorenz system. The results presented in this paper contain all the existing relative results as special cases.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2008.10.008