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