UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

Bifurcation of Bounded Solutions of Impulsive Differential Equations

Thumbnail Image

Files

10.1142S0218127416502424.pdf (442.88 KB)

Date

2016-12-30

Authors

Church, Kevin E. M.
Liu, Xinzhi

Journal Title

Journal ISSN

Volume Title

Publisher

World Scientific Publishing

Abstract

In this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular nonlinear integral operator whose zeroes coincide with bounded solutions of the impulsive differential equation in question. This leads to sufficient conditions for the presence of fold, transcritical and pitchfork bifurcations. Additionally, we provide a computable necessary condition for bifurcation in nonlinear scalar impulsive differential equations. Several examples are provided illustrating the results.

Description

Electronic version of an article published as International Journal of Bifurcation and Chaos, Volume 26, No. 14, 2016, 1-20 doi:10.1142/S0218127416502424 © copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0218127416502424

Keywords

Impulsive differential equations, bifurcation, bounded solution, hyperbolicity, exponential dichotomy

LC Keywords

Citation

URI

http://dx.doi.org/10.1142/S0218127416502424
 http://hdl.handle.net/10012/13151

Collections

Waterloo Research
Applied Mathematics