Critical diapause portion for oscillations: Parametric trigonometric functions and their applications for Hopf bifurcation analyses

TitleCritical diapause portion for oscillations: Parametric trigonometric functions and their applications for Hopf bifurcation analyses
Publication TypeJournal Article
Year of Publication2019
AuthorsZhang X, Wu J
JournalMath Meth Appl Sci
Volume42
Start Page1363
Pagination1363-1376
Date Published01/2019
Abstract

We introduce the concept of parametric trigonometric functions (convex combinations of two trigonometric functions with different oscillation frequencies) and explore their qualitative properties to derive an explicit formula of the critical diapause portion for the Hopf bifurcation to take place. Our work shows analytically that diapause can generate complex oscillations even though seasonality is not included.

URLhttps://onlinelibrary.wiley.com/doi/10.1002/mma.5424