Paper Info
Title
LOR for Analysis of Periodic Dynamics: A One-Stop Shop Approach
Abstract
A recently introduced technique, local orthogonal rectification (LOR), provides a way to derive coordinate systems that are tailored to locating objects of interest within flows in arbitrary dimensions. In this work, we apply LOR to identify periodic orbits and study the transient dynamics nearby. In the LOR method, the standard approach of finding periodic orbits by solving for fixed points of a Poincare return map is replaced by the solution of a boundary value problem with fixed endpoints, and the computation provides information about the stability of the identified orbit. We detail the general method and derive theory to show that once a periodic orbit has been identified with LOR, the LOR coordinate system allows us to characterize the stability of the periodic orbit, to continue the orbit with respect to system parameters, to identify invariant manifolds attendant to the periodic orbit, and to compute the asymptotic phase associated with points in a neighborhood of the periodic orbit in a novel way. All of this analysis can be done in a computationally synergistic manner within the "one-stop shop" of the LOR framework. We illustrate these ideas, along with the importance of the invariant manifolds for organizing the flow in the approach to a stable periodic orbit in R-3, using the Goodwin oscillator and a polynomial system featuring a period-doubling bifurcation.
Year
DOI
Venue
2020
10.1137/19M1258529
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Keywords
DocType
Volume
periodic orbit,transient dynamics,invariant manifolds,blow-up,coordinate transformation
Journal
19
Issue
ISSN
Citations 
1
1536-0040
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Benjamin Letson101.01
Jonathan E. Rubin223531.34