Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response

Abstract

Recently, Christian Cortés García proposed and studied a continuous modified Leslie–Gower model with harvesting and alternative food for predator and Holling-II functional response, and proved that the model undergoes transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation. In this paper, we dedicate ourselves to investigating the bifurcation problems of the discrete version of the model by using the Center Manifold Theorem and bifurcation theory, and obtain sufficient conditions for the occurrences of the transcritical bifurcation and Neimark–Sacker bifurcation, and the stability of the closed orbits bifurcated. Our numerical simulations not only illustrate corresponding theoretical results, but also reveal new dynamic chaos occurring, which is an essential difference between the continuous system and its corresponding discrete version.

The Spatiotemporal Dynamics of Insect Predator–Prey System Incorporating Refuge Effect

“…(31) According to the Caldano formula, the above one-dimensional cubic Equation (30) can be equated to (m…”

“…In most prior studies, the Holling type II predator–prey models were continuous and analyzed by phase plane and bifurcation diagrams, without integrating ecological phenomenon to analyze dynamic behaviors [ 25 , 26 , 27 ]. Although some scholars discretized the Holling type II model, the chaotic phase plane diagrams failed to be further distinguished [ 28 , 29 , 30 ]. These gaps have largely hindered our explorations of the complexity in insect predator–prey systems, thus further studies on the discrete Holling type II models are urgently needed.…”