Lecture Notes on Numerical Analysis of Nonlinear Equations
Numericalintegrators can providevaluable insight into the transient behavior of a dynamical system.However, when the interest isin stationary and periodic solutions, their stability, and their transition to more complex behavior, then numerical continuation and bifurcation techniques are very powerful and efficient.
The objective of these notes is to make the reader familiar with the ideas behind some basic numerical continuation and bifurcation techniques. This will be useful, and is at times necessary, for the effective use of the software Autoand other packages, such as XppAut, Content, Matcont, and DDE-Biftool, which incorporate the same or closely related algorithms.
These lecture notes are an edited subset of material from graduate courses given by the author at the universities of Utah and Minnesota  and at Concordia University, and from short courses given at various institutions, including the Université Pierre et Marie Curie (Paris VI), the Centre de Recherches Mathématiques of the Université de Montréal, the Technische Universität Hamburg-Harburg, and the Benemérita Universidad Autónoma de Puebla.
KeywordsPeriodic Solution Periodic Orbit Hopf Bifurcation Bifurcation Diagram Implicit Function Theorem
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