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Permanent URI for this collectionhttps://ds.uofallujah.edu.iq/handle/123456789/99

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    Design an efficient neural network for solving steady state problems
    (Elsevier, 2024-09) Ashraf Adnan Thirthar; Luma N. M. Tawfiq; Kamal Shah; Thabet Abdeljawad
    In this article, the mathematical model of steady state problems based on horizontal radial flow in homogenous confined aquifers has been presented. Then we design efficient neural network (ANN) to solve the equation in polar coordinates. A reliable unconstrained optimization method has been used as training algorithm to get high accuracy results. The results illustrated by contour maps. The new effective Levenberg-Marquardt method (NLM) has been implemented to solve the problem. A comparison between the training, testing and validation results has been presented. The weight of the ANN will be chosen such that satisfied local minimizer. Furthermore, the quadratic convergence of NLM has been proved. The results reveal that the suggested design is effective, time saver, and applicable for solving steady state problems.
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    Effects of predator cooperation in hunting and prey fear in a generalist predator–prey model that includes global warming phenomena
    (Springer Nature, 2024-11-26) Ashraf Adnan Thirthar; Bipin Kumar; Sushil Kumar Verma
    Emissions of greenhouse gases from humanactivities are the cause of global warming. Some of the repercussions include habitat loss, altered competitive relationships, and temperature and ecosystem changes that are too large for migration. According to this study, the carrying capacity is affected by global warming. Furthermore, by developing a predation function that accounts for the effects of hunting cooperation and global warming, its influence on predation has been examined. The interaction between prey, predators, and global warming is described by a system of ordinary differential equations that includes the components listed above. During our investigation, we examine the existence and stability of equilibrium points, which reveals the model’s dynamic behaviors. Our model shows a range of bifurcations, including Hopf, transcritical, and saddle-node bifurcations, which mark critical shifts in system dynamics. To confirm these bifurcations, we derive and verify transversality conditions. Additionally, we construct one- and two-parameter bifurcation diagrams to visualize stability changes across the parameter space, identifying regions with distinct steady states and dynamic behaviors. Notably, our model also exhibits switching behavior, where shifts in parameters lead to transitions between different dynamic states, highlighting the complexity and richness of prey-predator interactions.
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    The modified predator–prey model response to the effects of global warming, wind flow, fear, and hunting cooperation
    (Springer Nature, 2024-11-11) Ashraf Adnan Thirthar; Shireen Jawad; Muhammad Aqib Abbasi
    Global warming has a serious impact on the survival of organisms. Very few studies have considered the effect of global warming as a mathematical model. The effect of global warming on the carrying capacity of prey and predators has not been studied before. In this article, an ecological model describing the relationship between prey and predator and the effect of global warming on the carrying capacity of prey was studied. Moreover, the wind speed was considered an influencing factor in the predation process after developing the function that describes it. From a biological perspective, the nonnegativity and uniform bounded of all solutions for the model are proven. The existence of equilibria for the model and its local stability is investigated. The proof that the model has no periodic solution is studied, and the backward Hopf bifurcation analysis of the positive equilibrium point. Through numerical results, we can analyze the impact of periodic and chaotic nature on the species population. Furthermore, to confirm the complex dynamics like bifurcation and oscillation the numerical simulation plays an important role. Furthermore, this also helps us to visualize the dynamic results of the model. Here, we also present different numerical outcomes in terms of other parameters.