This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of a

This study has been focused on the detection of phenolic compound in aerial parts (stem and leaves)of the species belonging the genus Arabis L. A.Caucasica Willd, A.Sagittata (Bertol)DC, A.Aucheri Boiss, A.nova Vill of family cruciferou (Brassicaceae) which were collected during field trips of the districted of Iraq. Phenolic compounds have been identified by using High Performance Liquid Chromatography (HPLC). Nine standard compounds used for comparison five of them flavonoids ( Rutin, Quercetin, kaempferol, Luteolin and Apigenin) and the other phenolic acid ( Chlorogenic acid, Caffeic acid, Ferulic acid and Rosmarinic acid) , results showed that species vary in containing phenolic compound which can be counted as a taxonomic evidence s

In this paper a prey-predator model involving Holling type IV functional response
and intra-specific competition is proposed and analyzed. The local stability analysis of
the system is carried out. The occurrence of a simple Hopf bifurcation is investigated.
The global dynamics of the system is investigated with the help of the Lyapunov
function and poincare-bendixson theorem. Finally, the numerical simulation is used to
study the global dynamical behavior of the system. It is observed that, the system has
either stable point or periodic dynamics.

For the first time in Iraq, the crustacean Ergasilus ogawai Kabata,

1992 was recorded from the gills of Silurus triostegus, Mastacembelus mastacembelus, Mystus pelusius and Acanthopagrus latus out of 12 fish species caught from Garmat Ali river north of Basrah city during the period from September 1999 till August 2000. The percentage incidence of infestations of these four fish species were 98.9%, 100%,

49.6% and 71.4% while the intensity of infestations were 417, 81.8,

3.4 and 2, respectively. No significant differences in infestations of

male and female hosts  with this crustacean were detected.

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simul

In this work, we study two species of predator with two species of prey model, where the two species of prey live in two diverse habitats and have the ability to group-defense. Only one of the two predators tends to switch between the habitats. The mathematical model has at most 13 possible equilibrium points, one of which is the point of origin, two are axial, tow are interior points and the others are boundary points. The model with , where n is the switching index, is discussed regarding the boundedness of its solutions and the local stability of its equilibrium points. In addition, a basin of attraction was created for the interior point. Finally, three numerical examples were given to support the theoretical results.

<p>The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability

In this paper, an eco-epidemiological model with media coverage effects is established and studied. An -type of disease in predator is considered.  All the properties of the solution of the proposed model are discussed. An application to the stability theory was carried out to investigate the local as well as global stability of the system. The persistence conditions of the model are determined. The occurrence of local bifurcation in the model is studied. Further investigation of the global dynamics of the model is achieved through using a numerical simulation.