Browsing by Author "Gokgoz, Nurgul"

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A Chain Rule for Reduced Functional Differential Inclusions and Stability Theorems
(2025) Gokgoz, Nurgul
In order to represent real-world problems, modeling and stability concepts of a system are two essential steps, and functional differential inclusions become favorable among other methods because of their flexibility and robustness to handle those problems. Thus, functional differential inclusions (FDIs) provide a solid foundation for engineering problems, and the calculation of their derivatives becomes an important issue in checking the stability of them. Especially, to check the Lyapunov stability, various chain rules for FDIs are defined in the literature. In this work, a new chain rule is introduced in terms of the reduction procedure, a comparison with another one is represented, and the stability theorems in terms of Lyapunov are extended to the reduced functional differential inclusions.
For a Depensatory Fishery System Hybrid Modeling and Optimal Control of Harvest Policies
(2025) Cıfdaloz, Oguzhan; Gokgoz, Nurgul
Recent decades have brought an increasing concern for the sustainability of renewable resources, such as agricultural land, freshwater, forests, and fisheries. Management and control of them have been conducted through some institutions and governments, which mainly focus on efficiently managing those resources since they are affected by social and ecological uncertainties like climate change, difficulty in the application strategies, or uncertainties and noise in the data collection. Control engineering procedures represent a flexible and reasonable way to investigate and solve the difficulties, uncertainties, and noise listed above by formulating the problem mathematically. In this work, we investigate fisheries and revenue optimization by using a hybrid model. The harvest of the fishery is done during some seasons of the year, which suggests that the model should include both discrete and continuous dynamics. To investigate the bio-economic system, the problem is formulated by two-hybrid dynamical fishery models. Those formulations are used to investigate optimal control and the stability of the sustainability of the system. In this respect, we investigate the optimal effort for the maximization of the revenue where the continuation of sustainability is preserved. Moreover, which parameters should be taken into account to check the stability in this case are determined. Whenever the system is unstable, the optimal effort for the sustainability of the system is determined.
Forecasting Covid-19 Cases in Türkiye With the Help of Lstm
(2023) Gokgoz, Nurgul
Even though, it is thought that the pandemic has come to an end, the humanity is still under the danger of upcoming pandemics. In that sense, every effort to understand or predict the nature of an infectious disease is very precious since those efforts will provide experience for upcoming infectious disease epidemic/pandemic. Mathematical models provide a common way to analyze the nature of the pandemic. Apart from those mathematical models that mostly determine which variables should be used in the model to predict the nature of the epidemic and at which rate the disease will spread, deep learning models can also provide a fast and practical tool. Moreover, they can shed a light on which variables should be taken into account in the construction of a mathematical model. And also, deep learning methods give rapid results in the robust forecasting trends of the number of new patients that a country will deal with. In this work, a deep learning model that forecasts time series data using a long short-term memory (LSTM) network is used. The time series data used in this project is COVID-19 data taken from the Health Ministry of Republic of Türkiye. The weekend isolation and vaccination are not considered in the deep learning model. It is seen that even though the graph is consistent and similar to the graph of real number of patients, and LSTM is an effective tool to forecast new cases, those parameters, isolation and vaccination, must be taken into account in the construction of mathematical models and also in deep learning models as well.
Generalized Chebyshev Acceleration
(Springer, 2025) Gokgoz, Nurgul
We use generalized Chebyshev polynomials, associated with the root system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_2$$\end{document}, to provide a new semi-iterative method for accelerating simple iterative methods for solving linear systems. We apply this semi-iterative method to the Jacobi method, and give an example. We also analyze the efficiency of our method with sparse matrices of large dimension. There are certain restrictions but the resulting acceleration is rather high.