In this paper, we study the incorporation of the commensalism interaction and harvesting on the Lotka–Volterra food chain model. The system provides one commensal prey, one harvested prey, and two predators. A set of preliminary results in local bifurcation analysis around each equilibrium point for the proposed model is discussed, such as saddle-node, transcritical and pitchfork. Some numerical analysis to confirm the accruing of local bifurcation is illustrated. To back up the conclusions of the mathematical study, a numerical simulation of the model is carried out with the help of the MATLAB program. It can be concluded that the system's coexistence can be achieved as long as the harvesting rate on the second prey population is lower than its intrinsic growth rate. Further, the role of mutual interaction can lead to the stability of the proposed system.
The current research aims to determine the role of strategic leadership in achieving organizational excellence. In this context the sample of the research consist of 123 managers .The research problem can be summarized as {what is the role of strategic leadership in achieving organizational excellence}which resulted in a number of sub-questions and its goal was to explain the theoretical philosophy and intellectual expositions of this variables because of they are vital variables imposed by the current situation. To achieve research objectives we had use the questionnaire as a tool to collect data and information after verifying the validity and dependency of the measures. A number of statistical techniques and tools had been use
... Show MoreThis article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie
... Show MoreThe present study dealt with the morphological, anatomical,trichomespollen grains,and ecological characteristics of Caroxylon jordanicola (EigAkhani & Roalson (Amaranthaceae) in Al-Tar Caves, Karbala, Iraq which belongs to the Amaranthaceae family. The results of the present study demonstrated that There are distinctive characteristics of the studied species distinguish it from other species and facilitate its diagnosis. The sample was diagnosed using the taxonomic keys of the Iraqi flora and the flora of neighboring countriesIn addition to some available research. The results of the morphological and anatomical features investigation provide really significant taxonomical value to distinguish the species. The results that showe
... Show MoreIn this effort, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.