Bifurcation analysis and application for impulsive systems with delayed impulses
| dc.contributor.author | Church, Kevin E.M. | |
| dc.contributor.author | Liu, Xinzhi | |
| dc.date.accessioned | 2018-04-16T16:32:04Z | |
| dc.date.available | 2018-04-16T16:32:04Z | |
| dc.date.issued | 2017-11 | |
| dc.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 | en |
| dc.description.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. | en |
| dc.identifier.issn | 1793-6551 | |
| dc.identifier.uri | https://doi.org/10.1142/S0218127417501863 | |
| dc.identifier.uri | http://hdl.handle.net/10012/13091 | |
| dc.language.iso | en | en |
| dc.publisher | World Scientific | en |
| dc.subject | Bifurcation theory | en |
| dc.subject | impulsive delay differential equations | en |
| dc.subject | SIR model | en |
| dc.subject | logistic equation | en |
| dc.title | Bifurcation analysis and application for impulsive systems with delayed impulses | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Kevin E. M. Church and Xinzhi Liu, Bifurcation analysis and application for impulsive systems with delayed impulses, Int. J. Bifurcation Chaos 27, 1750186 (2017) | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Applied Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |
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