### Electronic Research Archive

2021, Issue 5: 3069-3079. doi: 10.3934/era.2021026
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# Instability and bifurcation of a cooperative system with periodic coefficients

• Received: 01 November 2020 Revised: 01 January 2021 Published: 16 March 2021
• Primary: 34C12, 34D99, 34A26, 34A40

• 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 $\lambda$ 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.

Citation: Tian Hou, Yi Wang, Xizhuang Xie. Instability and bifurcation of a cooperative system with periodic coefficients[J]. Electronic Research Archive, 2021, 29(5): 3069-3079. doi: 10.3934/era.2021026

### Related Papers:

• 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 $\lambda$ 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.

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