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

Author:

Zhang, X, and Wu, J

Publication type:

Journal Article

Publication date:

2019-01

Journal/Series title:

Math Meth Appl Sci

Volume:

URL:

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

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.