Qualitative analysis and control for predator-prey delays system

Xiaoxiao Chen and Xuedi Wang

Chaos, Solitons & Fractals, 2019, vol. 123, issue C, 361-372

Abstract: In this paper, the dynamics of a stage-structured predator-prey system with two time delays and Monod–Haldane response function are considered. By taking the two time delays as the bifurcation parameter, the local stability of the interior equilibrium is established and the conditions for existence of the Hopf bifurcation are obtained. Furthermore, based on the normal form method and center manifold theorem, the direction of the Hopf bifurcation and the stability of the bifurcation period solutions are investigated. In addition, by using parameter disturbance and state feedback control to act on the system, we succeeded in controlling the Hopf bifurcation of the original system. Numerical examples are given to carry out to support the obtained theoretical findings.

Keywords: Predator-prey system; Stage-structured; Time delays; Hopf bifurcation; Hybrid control (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:123:y:2019:i:c:p:361-372

DOI: 10.1016/j.chaos.2019.04.023

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