Dynamic analysis of a Leslie–Gower-type predator–prey system with the fear effect and ratio-dependent Holling III functional response

Abstract

In this paper, we extend a Leslie–Gower-type predator–prey system with ratio-dependent Holling III functional response considering the cost of antipredator defence due to fear. We study the impact of the fear effect on the model, and we find that many interesting dynamical properties of the model can occur when the fear effect is present. Firstly, the relationship between the fear coefficient K and the positive equilibrium point is introduced. Meanwhile, the existence of the Turing instability, the Hopf bifurcation, and the Turing–Hopf bifurcation are analyzed by some key bifurcation parameters. Next, a normal form for the Turing–Hopf bifurcation is calculated. Finally, numerical simulations are carried out to corroborate our theoretical results.

The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model

“…Since some objects in nature are not only changing with time but also have a difusion phenomenon in space, numerous mathematical models are combined with time and space, and we can call this type of models reaction-difusion models. In recent decades, the reaction-difusion model has been widely used and numerous experts and scholars have used it to study the dynamic behavior of various organisms in nature [1][2][3][4][5][6][7][8][9][10][11], and the results of these studies have played a positive role in environmental protection and governance.…”