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Qualitative analysis and control for predator-prey delays system. (English) Zbl 1448.92184

Summary: 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.

MSC:

92D25 Population dynamics (general)
93C23 Control/observation systems governed by functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K35 Control problems for functional-differential equations
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