Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/103063
Citations | ||
Scopus | Web of Science® | Altmetric |
---|---|---|
?
|
?
|
Type: | Journal article |
Title: | Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux |
Author: | Balasuriya, S. |
Citation: | Nonlinearity, 2016; 29(12):3897-3933 |
Publisher: | IOP Publishing |
Issue Date: | 2016 |
ISSN: | 0951-7715 1361-6544 |
Statement of Responsibility: | Sanjeeva Balasuriya |
Abstract: | State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses destroy the smooth invariant manifolds, necessitating new definitions for stable and unstable pseudo-manifolds. Their time-evolution is characterised by solving a Volterra integral equation of the second kind with discontinuous inhomogeniety. A criteria for heteroclinic trajectory persistence in this impulsive context is developed, as is a quantification of an instantaneous flux across broken heteroclinic manifolds. Several examples, including a kicked Duffing oscillator and an underwater explosion in the vicinity of an eddy, are used to illustrate the theory. |
Keywords: | stable and unstable manifolds; Dirac delta impulses; Volterra integral equation; nonautonomous dynamics; heteroclinic bifurcation; Melnikov theory; impulsive differential equation |
Rights: | © 2016 IOP Publishing Ltd & London Mathematical Society |
DOI: | 10.1088/0951-7715/29/12/3897 |
Grant ID: | http://purl.org/au-research/grants/arc/FT130100484 |
Published version: | http://dx.doi.org/10.1088/0951-7715/29/12/3897 |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
hdl_103063.pdf | Accepted version | 513.76 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.