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.
Despite the multiplicity of institutions contributing to the decision-making process in the United States of America, they interact to crystallize positions regarding international and strategic situations. The formulation of the national security policy depends on a number of institutions that complement each other in order to achieve an advanced security situation. Thus, the decision reflects the process of interaction of the existing regulatory institutions. This is because the essence of the national security and achieving its requirements also stems from the existence of a coherent system of shared beliefs and principles in the American society. Besides, these elements are the bases for achieving
... Show MoreThe study highlighted the transformation of value systems and educational patterns between past and present, especially with the introduction of modern variables and means, such as mobile phones, the internet, social media, and others. These factors have contributed both positively and negatively to the study. The study highlights the integral role of the school in collaboration with the family in guiding and educating children. It also emphasizes the active role of the school in developing students' abilities and skills, either attracting them to school or vice versa. This includes an examination of the essential skills required in education and their role in achieving a state of psychological well-being and systematically developing child
... Show MoreIn this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior
... Show MoreThe principle in the language is that each word has one meaning. This is because the purpose of language development is for understanding, understanding, and communication between people. The language is sounds with which each people expresses their Arabic language did not stop at this point, but rather needed another next stage or to convey additional features or characteristics that would qualify it. To be the language of the Qur’an and revelation, and capable of carrying this heavy burden.
النظام السياسي في كوريا الشمالة
Periodontitis is a persistent bacterial-causing disease which damages the supporting periodontium of the teeth. The complexity of supporting tissue structure makes the regeneration a challenge for periodontists. Early investigations were focused on discovering therapeutic substitutes that are biocompatible, simple to prepare and economic. This might cause a local release of growth factors that accelerate the healing process of the soft and hard tissue. Recently, platelet-rich fibrin (PRF) has received a wide attention as a biocompatible regenerative material in both dental and medical fields. PRF is a natural fibrin-derived biomaterial, and it is easy to obtain. It can be gotten from individual blood without the use of any external anticoag
... Show MoreThe current research attempts to examine the relationship between social-psychological conflict and their relation to family upbringing approaches among the adolescents of intermediate stage according to sex and economical level. To do this, the researcher prepared a questionnaire to measure social-psychological conflict that consisted of (32) item divided on four dimensions, and also she prepared a questionnaire to measure family upbringing approaches which composed of (28) item divided on four dimensions. The sample was (260) male and female student from intermediate stage chosen randomly. The results revealed that there were significant differences between social-psychological conflict which went to male, there was a negative correlat
... Show MoreABSTRACT
The multi-drug resistant efflux pump is a glycoprotein pump whose function is to push foreign substances. The efflux pump is found in humans, animals. It also has wide-ranging properties in bacteria and fungi. They are found in all species of bacteria, and efflux pump genes can be found in bacterial chromosomes or mobile genetic elements, such as plasmids. The most sensitive function that leads to a global problem is its resistance to antibiotics in bacterial cells, which increases the ability to bacteria from becoming strong virulence factors that most or all antibiotics cannot kill. It also has othe
... Show MoreAim of the Study: The paper aims at identifying the extent of the role of strategic leadership represented by its four dimensions (administrative, transformational, political, moral) in fulfilling the requirements of university governance (Context, message and Goal, Management orientation, Independence, Issue, Sharing)
Methodology: A survey is applied to (107) members of the teaching staff at the college of Administration and Economics/ University of Mosul. To achieve the goals of the study, the researcher makes use of a number of tools such as: questionnaire, statistical tools and methods (repetitions, perce
... Show MoreDiscriminant analysis is a technique used to distinguish and classification an individual to a group among a number of groups based on a linear combination of a set of relevant variables know discriminant function. In this research discriminant analysis used to analysis data from repeated measurements design. We will deal with the problem of discrimination and classification in the case of two groups by assuming the Compound Symmetry covariance structure under the assumption of normality for univariate repeated measures data.
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