The mathematical construction of an ecological model with a prey-predator relationship was done. It presumed that the prey consisted of a stage structure of juveniles and adults. While the adult prey species had the power to fight off the predator, the predator, and juvenile prey worked together to hunt them. Additionally, the effect of the harvest was considered on the prey. All the solution’s properties were discussed. All potential equilibrium points' local stability was tested. The prerequisites for persistence were established. Global stability was investigated using Lyapunov methods. It was found that the system underwent a saddle-node bifurcation near the coexistence equilibrium point while exhibiting a transcritical bifurcation

This study deals with the intellectual representations whose intellectual systems are incarnated in the Jewish personality, which is considered one of the complex intellectual systems that has caused controversy throughout the ages because of the ambiguity due to the religious and psychological factors that were reflected directly and strongly on the intellectual structure of the Jewish community in general and the Jewish - Zionist personality in particular, in an attempt (to create new dimensions embodied by intellectual representations of a human nature embodied by what that - peaceful - religiously oppressed - psychologically and socially isolated character presents, because of the curse of the peoples of the world that was a cause fo

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.

Modern statistical techniques offer a range of methodologies for modelling time series data, with conditional and unconditional approaches providing complementary insights that enhance overall model accuracy. This article introduced a modified ARIMA model employing conditional and unconditional parameter estimates. The methodology for the new model based on novel methods is provided. The prediction process, one and two steps ahead, is covered in detail, and a novel algorithm is presented. The best model is picked based on various measurement criteria, such as coefficient of determination (R2), root mean squared error (RMSE), and mean absolute scaled error (MASE). The suggested model is applied to a monthly petrol sales dataset (Jan

This work suggests a system of ordinary differential equations (ODEs) containing a three-species food chain model incorporating wind and fear effects. The properties of the solution, like positivity and bound-ness, were investigated. All equilibrium points (biologically feasible) have been obtained, and the local stability of these equilibriums has been carried out. The global stability outcomes on the equilibrium points under specific restrictions have been established. Also, the persistence restrictions have been investigated. By utilizing Sotomayor’s theorem, the local bifurcation of the suggested model has been inspected. Furthermore, numerical analysis was carried out to ensure the theoretical results obtained by utilizing MA