Abstract
A discrete-time Michaelis-Menten-type prey harvesting is discussed in this paper, in the modified Leslie-Gower predator-prey model. Detailed analysis of the topology of nonnegative interior fixed points is given, including their existence and stability dynamics. Also, the conditions for the existence of flip and Neimark-Sacker bifurcations are derived by using the center manifold theorem and bifurcation theory. The numerical simulations are provided, using a computer package, to illustrate the consistency of theoretical results.
Highlights
In order to implement the center manifold theorem, we assume that MC be the center manifold of (30), evaluated at ð0, 0Þ in a small neighborhood of K = 0
These values further complement the dynamics of our map, observed above and proves the correctness of Theorem 5
We get, Y1 = −0:23876 ≠ 0 and Y2 = 8:71736 ≠ 0. These values further complement the dynamics of our map, observed above and proved the correctness of Theorem 5
Summary
Received 10 September 2021; Revised 2 January 2022; Accepted 12 February 2022; Published 12 March 2022. The numerical simulations are provided, using a computer package, to illustrate the consistency of theoretical results
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