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Stability and bifurcation in a harvested one-predator–two-prey model with delays. (English) Zbl 1097.34051

This paper mainly concerns the stability and bifurcation of a delayed one-predator-two-prey model with harvesting of the predator at a constant rate. It is shown that time delay can cause a stable equilibrium to become unstable. By choosing the delay as a bifurcation parameter, Hopf bifurcation can occur as the delay crosses some critical values. The authors also investigate the direction and stability of the Hopf bifurcation by following the procedure of deriving a normal form given by T. Faria and L. T. Magalhães [J. Differ. Equations 122, No. 2, 181–200 (1995; Zbl 0836.34068)]. Finally, an example is given and numerical simulations are performed to justify the theoretical results.

MSC:

34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
92D40 Ecology
92D25 Population dynamics (general)

Citations:

Zbl 0836.34068
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References:

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