Elementary Stability and Bifurcation Theory
Published in December 1989
Book
Hardback
XXIII, 324 pages
978-3-540-97068-2 (ISBN)
Description
This second edition has been substantially revised. Its purpose is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. It is written not only for mathematicians, but for the broadest audience of potentially interested learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at a foundation level. Applications and examples are stressed throughout, and these were chosen to be as varied as possible.
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Content
Asymptotic solutions of evolution problems; bifurcation and stability of steady solutions of evolution equations in one dimension; imperfection theory and isolated solutions which perturb bifurcation; stability of steady solutions of evolution equations in two dimensions and n dimensions; appendices - bifurcation of steady solution in two dimensions and the stability of the bifurcating solutions; appendix - methods of projection for general problems of bifurcation into steady solutions; bifurcation of periodic solutions from steady ones (Hopf Bifurcation) in two dimensions; bifurcation of periodic solutions in the general case; subharmonic bifurcation of forced T-periodic solutions; subharmonic bifurcation of forced T-periodic solutions into asymptotically quasi-periodic solutions; appendix - secondary subharmonic and symptotically quasi-periodic bifurcation of periodic solutions (of Hopf's type) in the autonomous case; stability and bifurcation in conservative systems.