This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

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

Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

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.

The aim of this study was to propose and evaluate an eco-epidemiological model with Allee effect and nonlinear harvesting in predators. It was assumed that there is an SI-type of disease in prey, and only portion of the prey would be attacked by the predator due to the fleeing of the remainder of the prey to a safe area. It was also assumed that the predator consumed the prey according to modified Holling type-II functional response. All possible equilibrium points were determined, and the local and global stabilities were investigated. The possibility of occurrence of local bifurcation was also studied. Numerical simulation was used to further evaluate the global dynamics and the effects of varying parameters on the asymptotic behavior of

Research Summary :

         Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of the Messengers, his family and all his companions, then after:

     This is brief research that contained between its two covers one of the jurisprudence rules derived from Islamic Sharia that guarantees the right of others, in case of forcing to do the prohibited act, and it is a restriction of the rule: “Necessities allow prohibitions” and “Hardship brings facilitation” and support for the rule: “Necessities are valued.” It is an origin in alleviating the taxpayer definitely , and the study has briefly shown some of the jurisprudential appli

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.

The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.