1995 | OriginalPaper | Chapter
Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems
Author : Yuri A. Kuznetsov
Published in: Elements of Applied Bifurcation Theory
Publisher: Springer New York
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
This chapter is devoted to the study of generic bifurcations of fixed points of two-parameter maps. First we derive a list of such bifurcations. As for the final two bifurcations in the previous chapter, the description of the majority of these bifurcations is incomplete in principle. For all but two cases, only approximate normal forms can be constructed. Some of these normal forms will be presented in terms of associated planar continuous-time systems whose evolution operator φ1 approximates the map in question (or an appropriate number of iterates of the map). We present bifurcation diagrams of the approximate normal forms and discuss their relationships with the original maps.