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In this paper, we study a predator–prey model assuming that the prey population gathers together in herd and considering feeding satiation for the predator population as well. After analyzing the equilibrium points of the model, their stability and the existence of bifurcations we show the existence of multistability for three different equilibrium points via numerical simulations. This last analysis is performed using the bSTAB software and its extensions. It allows to compute the basin of stability values and to plot bifurcation diagram surfaces with respect to the model parameters. • A predator-prey model is studied assuming that the prey population gathers in herd. • The equilibrium points of the model are analyzed, as well as their stability. • We show the existence of multistability for three different equilibrium points. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the dynamical behaviors and stationary patterns of a diffusive modified Leslie–Gower predator–prey model with density-dependent motion in the predator population. We establish the existence of classical solutions with the uniform-in time bound and then analyze the local and global stability of the spatially homogeneous co-existence steady state under certain parametric conditions. By choosing the prey diffusion rate d 2 as the bifurcation parameter, the steady state bifurcations from the positive constant equilibrium solution are investigated. Numerical simulations are performed to corroborate our analytical findings. • We establish the existence of classical solutions for a diffusive modified Leslie–Gower predator prey model. • We analyze the local and global stability of the spatially homogeneous co-existence steady state. • The steady state bifurcations from the positive constant equilibrium solution are investigated. [ABSTRACT FROM AUTHOR]

In this paper, the influence of the fear effect and Leslie–Gower function on the dynamic behavior of the predator–prey model is considered. First, the well-posedness analysis of this model is demonstrated, and the existence and local stability of the equilibrium point are given. Then by using the bifurcation theory and selecting the appropriate bifurcation parameters, many types of bifurcation phenomena in the system are discovered, including transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. Meanwhile, the numerical simulations on the basis of theoretical analysis are further carried out to intuitively show the influence of fear effect on population. As the degree of fear increases, the system will undergo multiple dynamic behaviors switching until the final extinction of prey population, while the predator population will survive due to the presence of substitute prey. In addition, the initial density of predator and prey can determine whether the solution of system tends to a coexisting steady state or a periodic oscillation. • A novel prey–predator model with the impact of fear is introduced. • The system can experience many types of bifurcation phenomena. • Numerical simulations and sensitivity analysis are performed. • Our results show that fear effect plays an important role on deriving the complex dynamics. [ABSTRACT FROM AUTHOR]

Competitive exclusion is a phenomenon that often occurs in ecology when two species compete for the same limited resource, while coexistence of predator and prey is required to sustain a predator–prey system. It is of great interest to examine if coexistence of intraguild predator and prey is possible when they are competing for the same resource. In this paper, we study competitive exclusion and coexistence in an intraguild predation model that incorporates species' mutual interference characterized by a Beddington–DeAngelis functional response. We derive conditions for competitive exclusion and conditions for coexistence of intraguild predator and prey. This is achieved by discussing the existence, local and global stability of all feasible equilibria and uniform persistence. Numerical simulations are carried out to explore effects of intraguild predator interference and intraguild predation strength on the coexistence modes of intraguild predator and prey. • Species' mutual interference is incorporated. • Conditions on competitive exclusion are derived. • Conditions on coexistence are derived. • The model exhibits three modes of coexistence. • Strong intraguild predator interference has a stabilizing effect. [ABSTRACT FROM AUTHOR]

• Analytical and numerical results are obtained for a three-species food chain model that incorporates the cost and benefit of anti-predator behaviours. • A fear effect term is rigorously derived, the impact of the fear is fully expounded. • A comparison of dynamic behavior with the existing models, some new findings are presented. • The results may provide some useful biological insights into ecosystems containing predator-prey interactions. In this paper a three-species food chain model is formulated to investigate the impact of fear. First, we derive the predator's functional response by using the classical Holling's time budget argument and formulate a three-species food chain model where the cost and benefit of anti-predator behaviours are included. Then we study the dissipativity of the system and perform analysis on the existence and stability of equilibria. At last, we use numerical simulations to more visually explore the effects of fear on three species. The results show that the predator's fear effect can transform the system from chaotic dynamics to a stable state. Our results may provide some useful biological insights into ecosystems containing predator-prey interactions. [ABSTRACT FROM AUTHOR]