Hopf Bifurcations in Nicholson’s Blowfly Equation are Always Supercritical-Reference-Cited by-同舟云学术

Hopf Bifurcations in Nicholson’s Blowfly Equation are Always Supercritical

Published:2021-04 Issue:05 Volume:31 Page:2150071
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Balázs István¹²,Röst Gergely³

Affiliation:

1. MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, H-6720, Hungary

2. Department of Mathematics, University of Klagenfurt, Universitätsstraße 65-67, Klagenfurt am Wörthersee, 9020, Austria

3. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, H-6720, Hungary

Abstract

We prove that all Hopf bifurcations in the Nicholson’s blowfly equation are supercritical as we increase the delay. Earlier results treated only the first bifurcation point, and to determine the criticality of the bifurcation, one needed to substitute the parameters into a lengthy formula of the first Lyapunov coefficient. With our result, there is no need for such calculations at any bifurcation point.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127421500711

Reference4 articles.

1. Hopf bifurcation for Wright-type delay differential equations: The simplest formula, period estimates, and the absence of folds

2. Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity

3. Hopf bifurcation analysis in a delayed Nicholson blowflies equation

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