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Bifurcation analysis and application for impulsive systems with delayed impulses

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Date

2017-11

Authors

Church, Kevin E.M.
Liu, Xinzhi

Journal Title

Journal ISSN

Volume Title

Publisher

World Scientific

Abstract

In this article, we present a systematic approach to bifurcation analysis of impulsive systems with autonomous or periodic right-hand sides that may exhibit delayed impulse terms. Methods include Lyapunov–Schmidt reduction and center manifold reduction. Both methods are presented abstractly in the context of the stroboscopic map associated to a given impulsive system, and are illustrated by way of two in-depth examples: the analysis of a SIR model of disease transmission with seasonality and unevenly distributed moments of treatment, and a scalar logistic differential equation with a delayed census impulsive harvesting effort. It is proven that in some special cases, the logistic equation can exhibit a codimension two bifurcation at a 1:1 resonance point.

Description

Electronic version of an article published in International Journal of Bifurcation and Chaos, Volume 27, Issue 12, November 2017, 1750186 [23 pages]. DOI: 10.1142/S0218127417501863, © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ijbc

Keywords

Bifurcation theory, impulsive delay differential equations, SIR model, logistic equation

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Citation

URI

https://doi.org/10.1142/S0218127417501863
 http://hdl.handle.net/10012/13091

Collections

Waterloo Research
Applied Mathematics