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.

Some children are suffering from introversion in kindergartens , so it must be confront and obviated by specialists because it will inevitably lead to unsatisfactory results reflect negatively on the individual and the community together . And the introvert child is a miserable child incapable of social interaction or give - and - take with colleagues , lack of integration of the child to life leads to the obstruction of  participation with his peers in various activities.     Introversion  causes a real emotional deficit to the children of kindergartens which limits of possibility of their intellectual development and mental growth and that because of their isolation and poor focus in education

Background and objectives: This study aimed at testing the effect of plastic sleeve or barrier, used to cover the guide of the light cure unit to prevent cross-infection, on the shear bond strength and site of bond failure of stainless steel and ceramic orthodontic brackets. Materials and methods: Forty orthodontic brackets; twenty stainless steel and twenty ceramic brackets bonded to forty extracted human maxillary first premolars using light cure adhesive cured with and without the use of a protective plastic barrier on the guide. Comparing the effect of this barrier on the shear bond strength and adhesive remnant index was performed using an independent t-test and Chi-square test. Results: The protective barrier had decreased the shear b

This article investigates the decline of language loyalty in the age of audiovisual nearness. It is a socio-linguistic review of previous literature related to language disloyalty. It reviews the current theoretical efforts on the impact of audiovisual nearness created by social media and language loyalty. The descriptive design is used. The argument behind this review is that the audiovisual nearness provided by social media negatively affects language loyalty. This article concludes that the current theoretical efforts have paid much attention to the relationship between the audiovisual nearness and language loyalty. Such efforts have highlighted the fact that the social media platforms have provided unprecedented nearness that provoke in

The duty of care is the essence of the error of negligence under the English legal system, and without it, responsibility for negligence cannot be judged, regardless of the extent of the damage incurred. contained in English law. In view of the importance of proving the existence of the duty of care on the defendant so that it is possible to judge his responsibility for negligence, the need arises to find a general principle to which the defendant is subject in order to decide whether he owes the plaintiff with the duty of care and therefore responsible for the negligence, and this is what we will explain in the research topic the study.

Wives generally and working wives especially may encounter in some
families forms of physical or psychological violence through all the
levels or whether it was a psychological intimidation or cursing and
insolence and detracting her human . value and the husband marries
another woman or uses physical abuse against her and beating and
sexual abuse of the wife are also included in this from . it is noticed that
the violent attitude of the husband may take one from or it may change
and alter with time for it might lead to the increase of the possibility of
violence to occur in different ways
The importance of this study comes out from the step that on which in
folds the problem of the use of the husband of vio

The design studies, especially in their contemporary stages, have not been isolated from the subjects that underpin advanced ideas in the field of technical treatments that enrich and improve the social life of users through those technological innovations that have enhanced and changed life styles, Especially in the field of general institutional techniques, including cinemas, as the ideal places for people and visitors to this space, which can contribute to the promotion of cultural, social and technical aspects within this millennium. DONC as reflected on the positive communication and communication between the intellectual and cognitive develop individuals, including cultural and technical side of the individual. The first chapter co

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