Periodic orbits near equilibria via averaging theory of second order
DOI: https://doi.org/10.3846/13926292.2012.736090Abstract
Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differential system without assuming the existence of a first integral. Now, using averaging theory of the second order, we extend our result to the case when the first order average is identically zero. Our result can be interpreted as a kind of degenerated Hopf bifurcation.
Keywords:
differential equation, nonlinear differential equation, perturbation methodHow to Cite
Share
License
Copyright (c) 2012 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
View article in other formats
Published
Issue
Section
Copyright
Copyright (c) 2012 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.