This paper is concerned with a Holling-II stage-structured predator-prey system in which predators are divided into an immature and mature predators. The aim is to explore the impact of the prey's fear caused by the dread of mature predators in a prey-predator model including intraspecific competitions and prey shelters. The theoretical study includes the local and global stability analysis for the three equilibrium points of the system and shows the prey's fear may lead to improving the stability at the positive equilibrium point. A numerical analysis is given to ensure the accuracy of the theoretical outcomes and to testify the conditions of stability of the system near the non-trivial equilibrium points.

Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and und

In this paper, the conditions of persistence of a mathematical model, consists from
a predator interacting with stage structured prey are established. The occurrence of
local bifurcation and Hopf bifurcation are investigated. Finally, in order to confirm
our obtained analytical results, numerical simulations have been done for a
hypothetical set of parameter values .

It is proposed and studied a prey-predator system with a Holling type II functional response that merges predation fear with a predator-dependent prey's refuge. Understanding the impact of fear and refuge on the system's dynamic behavior is one of the objectives. All conceivable steady-states are investigated for their stability. The persistence condition of the system has been established. Local bifurcation analysis is performed in the Sotomayor sense. Extensive numerical simulation with varied parameters was used to explore the system's global dynamics. A limit cycle and a point attractor are the two types of attractors in the system. It's also interesting to note that the system exhibits bi-stability between these 2 types of attractors.

      In this paper, the interplay among four population species is offered. The system consists of two competitive prey, predator and super predators. The application of the hypothesis of the Sotomayor theorem for local bifurcation around every equilibrium point is adopted. It is detected that the transcritical bifurcation could occur near most of the system's equilibrium points, while saddle-node and pitchfork bifurcation can not be accrued at any of them. Further, the conditions that guarantee the accruing Hopf bifurcation are carried out. Finally, some numerical analysis is illustrated to confirm the analytical results.