The dynamical behavior of a two-dimensional continuous time dynamical system describing by a prey predator model is investigated. By means of constructing suitable Lyapunov functional, sufficient condition is derived for the global asymptotic stability of the positive equilibrium of the system. The Hopf bifurcation analysis is carried out. The numerical simulations are used to study the effect of periodic forcing in two different parameters. The results of simulations show that the model under the effects of periodic forcing in two different parameters, with or without phase difference, could exhibit chaotic dynamics for realistic and biologically feasible parametric values.

This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.

Abstract

This research aims to develop a unit as part of a sixth-grade Arabic language textbook and measure its effectiveness in the development of twenty-first-century skills of female students. The author adopted the experimental approach with a quasi-experimental design of the pre-post single-group. A list of the major skills was derived from the framework for the 21st-century skills of the mother tongue that was developed by the Partnership for 21st-Century Skills and reviewed and adjusted by some specialists. According to their views, the unit was developed. The study targeted 15 sub-skills falling under three main skills. The results of the study showed the effectiveness of the developed unit in the develo

God Almighty set out to build mosques, and he commanded to seek their architecture, and the competition for them, and allocate them with types of worship that are not valid in others, and to preserve their sanctity and not to be degraded and taken for mundane purposes and special benefits, because they are considered one of the most prominent features of Islam and the rituals of Islamic society, so this research came to show the rule Sharia in various and contemporary issues that are needed by the imams of the mosques, their rulers, and those responsible for them. Among the issues in which they have examined comparative juristic research and reached the most correct opinion are:
Building mosques over or under buildings and factories i

This research aims at building a proposed training program according to the self-regulated strategies for the mathematics teachers and to identify the effect of this program on relational Mathematics of teachers. The sample of the research was (60) Math teachers; (30) teachers as experimental group and (30) teachers as control group. The results of the current research reacheded that the proposed training program according to some self-managed learning strategies, meets the needs of trainees with remarkable effectiveness to improve the level of their teaching performance to achieve the desired goals. Training teacher according to self-managed learning strategies is effective in bringing about the transition of training to their students

Iraq suffers from lack of water resources supply because the headwaters of the rivers located outside its borders and the influence of upstream countries on the quantities of flowing water, in addition to the increase of pressure on available water as a result of population increase and not adopting the principle of rationalization where misuse and wastage and lack of strategic vision to treat and manage water use in accordance with the economic implications fall.  This is reflected fallout on water security and subsequently on national and food security, while the issue of using water resources is development top priority in different countries in the world because of the importance of water effect on the security of indivi

The current research aims to identify the level of digital skills of kindergarten teachers, identify the level of professional competence of kindergarten teachers, as well as to identify the relationship between digital skills and the professional competence of kindergarten teachers. The current research was determined by kindergarten teachers in the second Baghdad / Karkh Education Directorate for the academic year (2021-2022). The research sample consisted of (100) teachers chosen in a simple random way. To achieve the objectives of the research, the researcher developed a digital skills scale of (20) items and a scale of professional competence consisting of (22) items. The results revealed that kindergarten teachers have a high level

The research gained its importance from the importance of technical reserves in the insurance activity and its impact on the result of the activity of insurance companies and their financial position and thus reflected on the insurance prices as the technical reserves are one of the most important and most valuable budget items usually, as well as that the insurance activity has a role in maintaining economic development where some countries develop laws and instructions for the formation of those reserves binding application to insurance companies and the fact that the financial statements in general are of interest to shareholders, banks, the General Tax Authority and other beneficiaries In the insurance activity as policyholders and t

In this paper, compared eight methods for generating the initial value and the impact of these methods to estimate the parameter of a autoregressive model, as was the use of three of the most popular methods to estimate the model and the most commonly used by researchers MLL method, Barg method  and the least squares method and that using the method of simulation model  first order autoregressive through the design of a number of simulation experiments and the different sizes of the samples.

Corrosion of steel reinforcement is one of the biggest problems facing all countries in the world like bridges in the beach area and marine constructions which lead to study these problems and apply some economical solutions. According to the high cost of repair for these constructions, were studied the effect of using kind of chemical compounds sodium nitrite(NaNO₂) and sodium silicate(Na₂SiO₃) as corrosion inhibitors admixture for steel bars that immersed partially in electrolyte solution (water + sodium chloride in 3% conc.) (Approximately similar to the concentration of salt in sea water). The two inhibitors above added each one to the electrolyte solution at concentrations (0.5%, 1% and 2%) for both