Nonlinear bifurcation: Theory and Computation

Author: Yang Zhonghua
Publisher:
Publish Date: 2007-01-01
Features: This book systematically introduces the bifurcation theory and its computation that play a significant role in the process where nonlinear problems transition from order to chaos. It focuses on the classification and determination of singular points, the pseudo-arclength continuation method, the switching of solution branches, and other computational techniques for handling singularities in bifurcation calculations. The book also covers the computation of Hopf bifurcation, periodic solutions, and bifurcation, as well as the computation of homoclinic and heteroclinic orbits, Liapunov exponents, strange attractors, and fractal dimensions, which are computational methods in global bifurcation and chaos dynamics. This book can serve as a graduate textbook for students in applied mathematics, computational mathematics, nonlinear science, and related fields, as well as a selective course textbook for senior undergraduate students in these disciplines. Additionally, it can be used as a reference book for scientific computing professionals and researchers.