Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles

• Main Authors: Han, Maoan (Author), Yu, Pei (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2012.
• Series: Applied Mathematical Sciences, 181
• Subjects: Mathematics.; Approximation theory.; Dynamics.; Ergodic theory.; Differential equations.; Computer software.; Statistical physics.; Dynamical Systems and Ergodic Theory.; Approximations and Expansions.; Ordinary Differential Equations.; Mathematical Software.; Nonlinear Dynamics.

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  is integral to the theory of bifurcati...

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.