This paper treats the interactions among four population species. The system includes one mutuality prey, one harvested prey and two predators. The four species interaction can be described as a food chain, where the first prey helps the second harvested prey. The first and the second predator attack the first and the second prey, respectively, according to Lotka-Volterra type functional responses. The model is formulated using differential equations. One equilibrium point of the model is found and analysed to reveal a threshold that will allow the coexistence of all species. All other equilibrium points of the system are located, with their local and global stability being assessed. To back up the conclusions of the mathematical analysis, a numerical simulation examination of the model is carried out. The system's coexistence can be achieved as long as the harvesting rate of the prey population is lower than its intrinsic growth rate.
Abstract:
This research aims to identify the actual reality of the supply chain processes applied in the Noor Al-Kafeel Food Products Company, which was chosen as a research sample by measuring the application and documentation gap. The current research relies on the case study method to reach the desired results, and the seven-scale scale was relied on to identify the reality of the supply chain operations applied in the researched company and the use of quantitative and qualitative methods in data collection and analysis, as quantitative methods such as the arithmetic mean were used weighted, percentage measurement, and g
... Show MoreIn this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
In this paper, the interplay among four population species is offered. The system consists of two competitive prey, predator and super predators. The application of the hypothesis of the Sotomayor theorem for local bifurcation around every equilibrium point is adopted. It is detected that the transcritical bifurcation could occur near most of the system's equilibrium points, while saddle-node and pitchfork bifurcation can not be accrued at any of them. Further, the conditions that guarantee the accruing Hopf bifurcation are carried out. Finally, some numerical analysis is illustrated to confirm the analytical results.
In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.
In this study, the harvest of maize silage with the cross double row sowing method were tested with a single row disc silage machine in two different PTO applications (540 and 540E min-1) and at two different working speeds v1, v2 (1.8 and 2.5 km h-1). The possibilities of harvesting with a single row machine were revealed, and performance characteristics such as hourly fuel consumption, field-product fuel consumption and PTO power consumption were determined in the trials. The best results in terms of hourly fuel consumption and PTO power consumption were determined in the 540E PTO application and V1 working speed. When the fuel consumption of the field-product is evaluated, it is obtained with V2 working speed and 540E PTO application. As
... Show MoreFor a mathematical model the local bifurcation like pitchfork, transcritical and saddle node occurrence condition is defined in this paper. With the existing of toxicity and harvesting in predator and prey it consist of stage-structured. Near the positive equilibrium point of mathematical model on the Hopf bifurcation with particular emphasis it established. Near the equilibrium point E0 the transcritical bifurcation occurs it is described with analysis. And it shown that at equilibrium points E1 and E2 happened the occurrence of saddle-node bifurcation. At each point the pitch fork bifurcation occurrence is not happened.
In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect
... Show MoreAn integrated GIS-VBA (Geographical Information System – Visual Basic for Application), model is developed for selecting an optimum water harvesting dam location among an available locations in a watershed. The proposed model allows quick and precise estimation of an adopted weighted objective function for each selected location. In addition to that for each location, a different dam height is used as a nominee for optimum selection. The VBA model includes an optimization model with a weighted objective function that includes beneficiary items (positive) , such as the available storage , the dam height allowed by the site as an indicator for the potential of hydroelectric power generation , the rainfall rate as a source of water . In a
... Show MoreThis in order to test the effect of food on growth and fecundity, two kinds of food have been used the algae Scendesmus quadricaudae and fresh water shrimp powder. For two generations, growth and productivity have been followed up. The fresh water shrimp has been noticed as a food better than algae, because it caused recording, for the two generation higher length rate for the weeks of experiment. The individuals length rate at the end of the forth week reached 9.35 and 9.48 mm for the first generation and second generation respectively. The average length weekly increase rate for the first and second generations individuals feeding on dried shrimp was higher through the first and second week compared to what was recorded when feeding alga
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