In this paper, a discrete- time ratio-dependent prey- predator model is proposed and analyzed. All possible fixed points have been obtained. The local stability conditions for these fixed points have been established. The global stability of the proposed system is investigated numerically. Bifurcation diagrams as a function of growth rate of the prey species are drawn. It is observed that the proposed system has rich dynamics including chaos.

Critical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge

‎  Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19    pandemic  ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemic has caused a ‎major global crisis, with 554,767 total confirmed cases, 484,570 total recovered cases, and ‎‎12,306 deaths in Iraq as of February 2, 2020. In the absence of any effective therapeutics or drugs ‎and with an unknown epidemiological life cycle, predictive mathematical models can aid in ‎the understanding of both control and management of coronavirus disease. Among the important ‎factors that helped the rapid spread of the ep

An eco-epidemiological system incorporating a vertically transmitted infectious disease is proposed and investigated. Micheal-Mentence type of harvesting is utilized to study the harvesting effort imposed on the predator. All the properties of the solution of the system are discussed. The dynamical behaviour of the system, involving local stability, global stability, and local bifurcation, is investigated. The work is finalized with the numerical simulation to observe the global behaviour of the solution.

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels

This survey investigates the thermal evaporation of Ag2Se on glass substrates at various thermal annealing temperatures (300, 348, 398, and 448) °K. To ascertain the effect of annealing temperature on the structural, surface morphology, and optical properties of Ag2Se films, investigations and research were carried out. The crystal structure of the film was described by Xray diffraction and other methods.The physical structure and characteristics of the Ag2Se thin films were examined using X-ray and atomic force microscopy (AFM) based techniques. The Ag2Se films surface morphology was examined by AFM techniques; the investigation gave average diameter, surface roughness, and grain size mutation values with increasing annealing temperature

This survey investigates the thermal evaporation of Ag2Se on glass substrates at various thermal
annealing temperatures (300, 348, 398, and 448) °K. To ascertain the effect of annealing
temperature on the structural, surface morphology, and optical properties of Ag2Se films,
investigations and research were carried out. The crystal structure of the film was described by Xray diffraction and other methods.The physical structure and characteristics of the Ag2Se thin films
were examined using X-ray and atomic force microscopy (AFM) based techniques. The Ag2Se
films surface morphology was examined by AFM techniques; the investigation gave average
diameter, surface roughness, and grain size mutation value

Thin films of ZnSe arc deposited on glass substrates by thermal evaporation in vacuum with different thickness (1000, 2700, 4000) A° temperature (293-373) °K are studies the electrical properties before and after annealing. The result show decrease D.0 conductivity and increasing the activation energy Eat.

In this work, the dynamic behavior of discrete models is analyzed with Beverton- Holt function growth . All equilibria are found . The existence and local stability are investigated of all its equilibria.. The optimal harvest strategy is done for the system by using Pontryagin’s maximum principle to solve the optimality problem. Finally numerical simulations are used to solve the optimality problem and to enhance the results of mathematical analysis

The goal of this paper is to study dynamic behavior of a sporadic model (prey-predator). All fixed points of the model are found. We set the conditions that required to investigate the local stability of all fixed points. The model is extended to an optimal control model. The Pontryagin's maximum principle is used to achieve the optimal solutions. Finally, numerical simulations have been applied to confirm the theoretical results.