The present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stability of the axial equilibrium point is discussed using the appropriate Lyapunov function, while the basin of attraction of the positive equilibrium point is investigated. The persistence constraints of the system are established. The local and Hopf bifurcation analyses of the system are examined. Lastly, numerical simulations are given to ensure the theoretical results with the help of Matlab program (version R2018b). It is found that the effect of fear plays a substantial role in the dynamic of the system. On the other hand, the refuge’s coefficient continuously affects the system. Furthermore, the variation of the refuge’s coefficient by utilizing different initial points leads to a change in the behavior of the system from stable to unstable and conversely.
In this study, the hydromorphodynamic simulation of a stretch of the Euphrates River was conducted. The stretch of the Euphrates River extended from Haditha dam to the city of Heet in Al-Anbar Governorate and it is estimated to be 124.4 km. Samples were taken from 3 sites along the banks of the river stretch using sampling equipment. The samples were taken to the laboratory for grain size analysis where the median size (D50) and sediment load were determined. The hydromorphodynamic simulation was conducted using the NACY 2DH solver of the iRIC model. The model was calibration using the Manning roughness, sediment load, and median particle size and the validation process showed that the error between th
... Show MoreIn this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth
... Show MoreMany studies and researchers have reported significant evidence that some physical properties of water can be changed as it passes through a magnetic field that can improve water use. This can have a promising potential for applications, especially in the fields of irrigation and drainage. In this research, magnetized water was used to leach salt-affected sandy loam soil. A test rig was designed and constructed to investigate the effects of magnetized water on leaching soil. The rig consists of a magnetization device that can provide variable intensity. Water was supplied from a constant head reservoir to the magnetization device then to the soils that were placed in plastic columns. Five different magnetic intensi
... Show MoreCooling towers is one of the most important unit in industry, they are used to dispose heat from cooling media used in the integrated units. The choice of the cooling media plays recently an important rule due to fresh-water scarcity. The use of saline as a cooling media become of growing interest, but the corrosion problem has to be taken in consideration. In this study the simultaneous effect of cooling tower operation parameters on the corrosion rate of mild-steel is considered. The role of NaCl content is found to be pronounced more than the working solution temperature and flowrate. The corrosion of mild-steel in these studied factors had shown an interesting result especially with the NaCl% content. Firstly, there was an increase in t
... Show MoreThe double-skin profiled composite wall (DSPCW) system, filled with concrete material, is favorable in modern structures due to its high strength and ductility. Openings may be required within this composite wall (DSPCW) for various reasons, similar to a conventional bearing wall, which can lead to a reduction in bearing capacity. Therefore, to avoid changes in the geometry, materials, and thickness of this DSPCW wall, a new internally stiffening concept has been suggested by providing embedded cold-formed steel tube (CFST) columns. For this purpose, two full-scale DSPCW specimens were tested under static axial load, one of which was fabricated with a large opening size and stiffened with two octagonal CFST columns, while the other
... Show MoreThis study aims to compare the response of reinforced concrete (RC) T-beams strengthened with carbon fibre-reinforced polymer (CFRP) composite with that of non-strengthened control beams when subjected to monotonic two-point loading until failure for flexural once and shear again. The experimental programme tested eight RC T-beams, which included two reference beams without strengthening and six strengthened beams. The eight beams were divided into two main groups according to strengthening (flexural and shear). Experimental analysis was performed to study the effect of the CFRP laminate width in the flexural group and the spacing of CFRP U-wrap sheets in the shear group on the ultimate load capacity, load-strain relationship, and l
... Show MoreSeveral attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope
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