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.
Phraseological or phraseological turn - unchanged in structure and composition, integral in meaning and lexically indivisible phrase or sentence, performing the function of a separate dictionary unit - lexemes. Idioms are found in any language of the world. But such a number of winged phrases, as in Russian, is nowhere else. Idioms play a role in displaying the national-cultural characteristics of any language. They very clearly and accurately reflect the characteristics of the perception of the world, the characteristic features of the material and spiritual life of native speakers, his mentality.
This study aimed to clarify the legal provisions concerning the senses and their role in financial transactions, in the light of the definition of all the vocabulary presented by this study (senses - the definition of senses apparent: they are hearing - sight - smell - taste - touch) in the first section. The study deals with the second topic of the reference and writing denominator phrase and includes two requirements, the first requirement: the establishment of the denominator of the phrase, which has two branches: Section I: signal Akhras. Section II: Signal of the Spokesman.
The second requirement is that writing takes the place of the phrase in financial transactions. The owners argue that the sale of the blind is correct a
This research tries to reveal how to manage and control the competitive edge for business by building managerial skills in various organizational levels. Our research aims at finding out the nature of various technical, human and in tellectual skills of a new president whose superiority is his competitive ness in the application field at general company for construe tioual industriesand testing the surveyed minor and major changes through a questionnaire to collect information from officials. The sample was composed of (45) director. The data was analyzed using some methods and statistical programs. The most prominent of these is (SPSS) that was used to extract the arithmetic mean, standard deviation, correlation coefficient
... Show MoreThe research topic (The dramatic structure transformations in the Iraqi Feature Film) studies the dramatic structure and its transformations in the Iraqi feature film. The research determined the research problem and the need for it in addition to the aims and the limits of the study as well as its importance. The theoretical framework consists of the following themes: the dramatic transformations mechanism and dramatic data in the Iraq film 1957-2003 then the dramatic values transformations and the performance contradictions in the Iraqi film.
The research, after concluding the theoretical framework, came up with a number of indicators of the theoretical framework that have been used as a tool to analyze the sample. The research proc
Metalloendo peptidase is a neutral endopeptidase that cleaves peptides at the amino side of hydrophobic residues and inactivates several peptide hormones, including atrial natriuretic factor, giucagon, enkephalin, substance p, neurotensin, oxytocin, and bradykinin. It is also a major enzyme for the degradation of beta-amyloid. This study aimed to measure enzyme activity and compare it with other biochemical changes in sera patients with diabetic nephropathy. The study included 35 pathological samples of people with diabetic nephropathy, 24 samples from males and 11 samples from females, as well as the same number of healthy people as a comparison group of 15 males, 20 females, with the ages of both groups of patients with diabetic nephropat
... Show MoreConstitutional Review of 1992 and 1996 and the role of the Party of Progress and Socialism