In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

Global warming has a serious impact on the survival of organisms. Very few studies have considered the effect of global warming as a mathematical model. The effect of global warming on the carrying capacity of prey and predators has not been studied before. In this article, an ecological model describing the relationship between prey and predator and the effect of global warming on the carrying capacity of prey was studied. Moreover, the wind speed was considered an influencing factor in the predation process after developing the function that describes it. From a biological perspective, the nonnegativity and uniform bounded of all solutions for the model are proven. The existence of equilibria for the model and its local stability is inves

A harvested prey-predator model with infectious disease in preyis investigated. It is assumed that the predator feeds on the infected prey only according to Holling type-II functional response. The existence, uniqueness and boundedness of the solution of the model are investigated. The local stability analysis of the harvested prey-predator model is carried out. The necessary and sufficient conditions for the persistence of the model are also obtained. Finally, the global dynamics of this model is investigated analytically as well as numerically. It is observed that, the model have different types of dynamical behaviors including chaos.

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.

We propose an intraguild predation ecological system consisting of a tri-trophic food web with a fear response for the basal prey and a Lotka–Volterra functional response for predation by both a specialist predator (intraguild prey) and a generalist predator (intraguild predator), which we call the superpredator. We prove the positivity, existence, uniqueness, and boundedness of solutions, determine all equilibrium points, prove global stability, determine local bifurcations, and illustrate our results with numerical simulations. An unexpected outcome of the prey's fear of its specialist predator is the potential eradication of the superpredator.

In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator.  e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated.  e su‰cient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to con‹rm the theoretical results.