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.

The increasing use of polymeric materials in the daily life, leads to challenges in the processing industry to deliver high performance materials with affordable terms. However, new processing techniques lead to high costs. In order to reduce processing costs it is necessary to understand the non-Newtonian behavior of the polymers in their molten state to be able to simulate the processes before the construction of the plants starts. Here the shear thinning behavior of the viscosity of polymeric melts is essential. Thus, this paper deals with the experimental investigation of the thermo-rheological behavior of the viscosity of one of the most used polymers (Polypropylene) over a wide range of temperatures and shear rates.  Furthermo

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 art of calligraphy is regarded as one of the tremendous and distinct products in the history of Islamic arts through the unparalleled high ranks it reached to, until it gained Islam's indication and became a symbol for it, in terms of its function linked to the calligraphy of the holy Qur'anic texts, where this merit formed a strong impulse in seeking its development, the emergence of the calligraphic constructs, including the calligraphic straps, is one of this continual seeking products, and an advanced stage at the level of technical and expressive development, and also one of the natural results generated by the development of fonts and the increase of their employing methods through what they recorded at the level of formal char

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

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.

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