Synopses & Reviews
Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus
Review
From the reviews: "This monograph written by excellent specialists in the fundamental theory of limit cycles represents an introduction to the most new developments and systematical presentation of major advances in this field which come mainly from the authors' own recent research results. ... Classic topics with recent results are presented in a clear and concise manner that will be suitable for post-graduate students studying the theory of limit cycles as well as for scientists interesting in the applications of periodic behavior." (Alexander Grin, Zentralblatt MATH, Vol. 1252, 2012)
Synopsis
This book introduces the recent developments in the field and provides major advances in fundamental theory of limit cycles. It considers near Hamiltonian systems using Melnikov function as the main mathematical tool.
Table of Contents
Hopf Bifurcation and Normal Form Computation.- Comparison of Methods for Computing Focus Values.- Application (I)--Hilbert's 16th Problem.- Application (II)--Practical Problems.- Fundamental Theory of the Melnikov Function Method.- Limit Cycle Bifurcations Near a Center.- Limit Cycles Near a Homoclinic or Heteroclinic Loop.- Finding More Limit Cycles Using Melnikov Functions.- Limit Cycle Bifurcations in Equivariant Systems.