Document Type
Report
Source Publication Title
Technical Report 148
Abstract
In Hopf bifurcation theory often an exchange of stability of an equilibrium gives rise to the creation of periodic orbits for a one parameter family of differential equations. In particular, let us consider the system in Rn given by [see pdf for notation] where µ E [0,^) for µ sufficiently small, a(µ), ß(µ) and Aµ are C°° in µ with a(0) = 0 and ß(0) = 1. Assume [see pdf for notation] where [see pdf for notation] and for each µ, X, Y, Z are of order greater than one at the origin. Finally, the eigenvalues [see pdf for notation] of the (n-2) x (n-2) matrix A0 satisfy the non-resonance condition [see pdf for notation]. We shall refer to the right hand sides of (10) and (1µ) as f0(x,y,z) and fµ (x,y,z) respectively.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
2-1-1981
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Bernfeld, Stephen R., "Generalized Transversality, Exchange of Stability and Hopf Bifurcation" (1981). Mathematics Technical Papers. 297.
https://mavmatrix.uta.edu/math_technicalpapers/297