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Hopf Bifurcations in Nicholson’s Blowfly Equation are Always Supercritical
International Journal of Bifurcation and Chaos ( IF 2.2 ) Pub Date : 2021-04-29 , DOI: 10.1142/s0218127421500711
István Balázs 1, 2 , Gergely Röst 3
Affiliation  

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.

中文翻译:

Nicholson 的 Blowfly 方程中的 Hopf 分岔总是超临界的

我们证明当我们增加延迟时,Nicholson 的苍蝇方程中的所有 Hopf 分岔都是超临界的。早期的结果只处理了第一个分岔点,为了确定分岔的临界点,需要将参数代入第一个 Lyapunov 系数的冗长公式。根据我们的结果,在任何分叉点都不需要进行此类计算。
更新日期:2021-04-29
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