In this paper, a mathematical model consisting of harmful phytoplankton and two competing zooplankton is proposed and studied. The existence of all possible equilibrium points is carried out. The dynamical behaviors of the model system around biologically feasible equilibrium points are studied. Suitable Lyapunov functions are used to construct the basins of attractions of those points. Conditions for which the proposed model persists are established. The occurrence of local bifurcation and a Hopf bifurcation are investigated. Finally, to confirm our obtained analytical results and specify the vital parameters, numerical simulations are used for a hypothetical set of parameter values.

Android operating system, since its first start, is growing very fast and takes a large space in smart devices market. It is built and developed on Linux and designed basically for touch screen devices such as, mobiles, tablets, etc. Mobile devices are markedly complicated and feature-rich; therefore they are prone to reliability of software and performance problems. Because of the small resources, smart devices, such as CPU, RAM, suffer from problems. One of these problems is Software Aging (SA). SA is recognized in long running OSs as a shortage in resources, performance retreating, and finally failure. SA is looked at from two sides, namely the poor response time of application which represents the end user side and the shortage in me

The research aims to achieve a set of the most important objectives of the review of the role of creative administrative leadership in achieving aspects of economic reform in various government institutions and indicate the role of supervisory awareness of administrative leadership in the revitalization of the role of the internal control system to achieve the best use of available resources. This paper deals with three problems is the loss of financial resources of the state as a result of the growing phenomenon of administrative and financial corruption in the majority of government institutions, and the weakness of the role of the internal control system in the province on the resources available and to achieve the best use of these reso

    The relationship between prey and predator populations is hypothesized and examined using a mathematical model. Predation fear, cannibalism among the prey population, and a refuge reliant on predators are predicted to occur. This study set out to look at the long-term behavior of the proposed model and the effects of its key elements. The solution properties of the model were investigated. All potential equilibrium points' existence and stability were looked at. The system's persistence requirements were established. What circumstances could lead to local bifurcation near equilibrium points was uncovered. Suitable Lyapunov functions are used to study the system's overall dynamics. Numerical simulations were conducted to verify the

     The dynamical behavior of an ecological system of  two predators-one prey updated with incorporating prey refuge and Beddington –De Angelis functional response had been studied in this work, The essential mathematical features of the present model have been studied  thoroughly. The system has local and global stability when certain conditions are met.  had been  proved respectively.  Further, the system has no saddle node bifurcation but transcritical bifurcation and Pitchfork bifurcation are satisfied while the Hopf bifurcation does not occur. Numerical illustrations are performed  to validate the model's applicability under consideration. Finally, the results are included in the form of points in agreement with the obt

The need for participants’ performance assessments in academia and industry has been a growing concern. It has attendance, among other metrics, is a key factor in engendering a holistic approach to decision-making. For institutions or organizations where managing people is an important yet challenging task, attendance tracking and management could be employed to improve this seemingly time-consuming process while keeping an accurate attendance record. The manual/quasi-analog approach of taking attendance in some institutions could be unreliable and inefficient, leading to inaccurate computation of attendance rates and data loss. This work, therefore, proposes a system that employs embedded technology and a biometric/ w

In this paper an eco-epidemiological system has been proposed and studied analytically as well as numerically. The boundedness, existence and uniqueness of the solution are discussed. The local and global stability of all possible equilibrium point are investigated. The global dynamics is studied numerically. It is obtained that system has rich in dynamics including Hopf bifurcation.

Passes the Arab order moment political precision of disruption and discord and
differences of countless between its components and its parts because of the suffering he
endured and the suffering now from internal disturbances as a result of lack of cohesion
relations intra-and cultural, historical and lack of interaction between these components so
that became the focus of the policies and interests is an unprecedented degree , reduced with
the joint Arab action to the minimum, and began to focus on the interests of special
regulations.
This is with regard suffering internally, but externally the regime Arab Regional is absent the
biggest influence on international decisions because of the courtesies which were ca