The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.

This study was conducted on a sample of commercial banks in Iraq, chosen according number of considerations for twenty banks, contained two public banks and eighteen private banks.                                                                                             &

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

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 deficit of the federal budget and the structural imbalances suffered by the Iraqi economy has affected the direction of research towards suggesting steps and mechanisms can be relied upon in the near term to form a broader base of non-oil revenues aimed at achieving a balanced budget, and to proceed to reform the financial situation, In reducing their financial dictates, whether capital or operational, which lead to significant financial and economic consequences. This also requires that the Iraqi political elite have the real will, strategic vision and full awareness that the implementation of these reforms has potential social and economic effects, with long-term measures to be taken. The aim is not only to reform the finan

ABSTRACT

The research focuses on the key issue concerning the use of the best ways to test the financial stability in the banking sector, considering that financial stability cannot be achieved unless  the financial sector in general and the banking sector  in particular are able to perform its key role in addressing the economic and social development requirements, under the laws and regulations that control  banking sector , as the only way that increases its ability to deal with any risks or negative effects experienced by banks and other financial institutions. The research goal is  to evaluate the stability of the banking system in Iraq, through the use of a set of econometrics an