About: Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations

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About: Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations Goto Sponge NotDistinct Permalink

An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations
Creator	Koonprasert, Sanoe Moore, Elvin Darlai, Rachadawan
Source	PMC
abstract	In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. For the seven different time-delay versions of each model, proofs are given of necessary and sufficient conditions for the existence and stability of equilibrium points and for the existence of Andronov–Hopf bifurcations in the differential equations and Neimark–Sacker bifurcations in the difference equations. We show that only five of the seven time-delay versions have bifurcations and that all bifurcation versions have supercritical limit cycles with one having a repelling cycle and four having attracting cycles. Numerical simulations are used to illustrate the analytical results and to show that critical times for Neimark–Sacker bifurcations are less than critical times for Andronov–Hopf bifurcations but converge to them as the time step of the discretization tends to zero.
has issue date	2020-04-29(xsd:dateTime)
bibo:doi	10.1186/s13662-020-02646-5
bibo:pmid	32435267
has license	cc-by
sha1sum (hex)	8ceaaa87a76db5f305006a242a690c597b302a5c
schema:url	https://doi.org/10.1186/s13662-020-02646-5
resource representing a document's title	Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations
has PubMed Central identifier	PMC7223581
has PubMed identifier	32435267
schema:publication	Adv Differ Equ
resource representing a document's body	covid:8ceaaa87a76db5f305006a242a690c597b302a5c#body_text
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