Abstract
In this paper, Hopf bifurcation is studied for a modified Leslie--Gower predator--prey system with harvesting. Our modified system is a biological economic cognitive system. An important feature of the biological economic cognitive system is that the harvest effort on the predator--prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theory, we obtain some new criteria for the Hopf bifurcation. Lastly, a numerical example is provided to demonstrate the effectiveness of our results.
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