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Stability region bifurcations of nonlinear autonomous dynamical systems: Type‐zero saddle‐node bifurcations
Author(s) -
Amaral F. M.,
Alberto L. F. C.
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1605
Subject(s) - saddle node bifurcation , bifurcation , stability (learning theory) , zero (linguistics) , mathematics , nonlinear system , node (physics) , boundary (topology) , saddle point , control theory (sociology) , type (biology) , saddle , mathematical analysis , physics , computer science , geometry , mathematical optimization , control (management) , ecology , linguistics , philosophy , quantum mechanics , machine learning , artificial intelligence , biology
The behavior of stability regions of nonlinear autonomous dynamical systems subjected to parameter variation is studied in this paper. In particular, the behavior of stability regions and stability boundaries when the system undergoes a type‐zero sadle‐node bifurcation on the stability boundary is investigated in this paper. It is shown that the stability regions suffer drastic changes with parameter variation if type‐zero saddle‐node bifurcations occur on the stability boundary. A complete characterization of these changes in the neighborhood of a type‐zero saddle‐node bifurcation value is presented in this paper. Copyright © 2010 John Wiley & Sons, Ltd.