On Hopf bifurcation and control for a delay systems

Xiaowei Jiang, Xiangyong Chen, Ming Chi and Jie Chen

Applied Mathematics and Computation, 2020, vol. 370, issue C

Abstract: Hopf bifurcation of a delay differential equation modeling two-enterprise interaction mechanism is investigated. For the demands of computer simulation applications, the discrete-time two-enterprise interaction model is proposed by using the forward Euler scheme. By discussing the characteristic equation of linearized part, the local stability criterion of the positive fixed point is presented. Time lag is selected as the bifurcation parameter. Then it is demonstrated that variation of time lag may result in Hopf bifurcation. Furthermore, derivations for the directions and stability of Hopf bifurcation are also given. For the purpose of controlling Hopf bifurcation, a time-delayed feedback control scheme is proposed. Finally, we simulate the main results.

Keywords: Hopf bifurcation; Time lag; Stability; Bifurcation control (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319308987

DOI: 10.1016/j.amc.2019.124906

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