Open AccessInstability and bifurcation of a cooperative system with periodic coefficients
Author(s) -
Hui Tian,
Yi Wang,
Xizhuang Xie
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021026
Subject(s) - bifurcation diagram , bifurcation , monotone polygon , mathematics , instability , focus (optics) , mathematical analysis , nonlinear system , physics , geometry , quantum mechanics , mechanics , optics
In this paper, we focus on a linear cooperative system with periodic coefficients proposed by Mierczyński [SIAM Review 59(2017), 649-670]. By introducing a switching strategy parameter \begin{document}$ \lambda $\end{document} in the periodic coefficients, the bifurcation of instability and the optimization of the switching strategy are investigated. The critical value of unstable branches is determined by appealing to the theory of monotone dynamical system. A bifurcation diagram is presented and numerical examples are given to illustrate the effectiveness of our theoretical result.