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    A new approach to determine occupational accident dynamics by using ordinary differential equations based on SIR model
    (Nature Portfolio, 2024) Kaplanvural, Selcan; Tosyali, Eren; Ekmekci, Ismail
    The motivation of this study is to develop and establish an occupational accident dynamical model (OA model) based on Susceptible-Infected-Recovered framework. In order to investigate the dynamics of the OA model, monthly occupational accident data from Turkey between 2013 and 2020 has been selected as dataset. The OA model is defined by a coupled first-order ordinary nonlinear differential equation with four variables. In addition, the relationships between these variables are described with ten parameters. The OA model's characterization of the equilibrium points is analyzed by investigating the behaviors of these points according to the eigenvalues derived from the Jacobian matrix. Also, the stability of these points is obtained according to the eigenvalues. These results show the behavior of the system near equilibrium points. After that, the reproduction number is computed by using the next-generation matrix method. The calculated reproduction number for given parameters reveals that the OA model is unstable. The OA model is numerically solved in 96 steps, with a time interval of 1 month, using the ODE45 Matlab routine based on the explicit Runge-Kutta algorithm. In addition, a modified OA model is developed by adding the Occupational Health and Safety (OHS) re-training parameter to the OA model to observe a reducing effect on occupational accident numbers. The main results of this study provide a new approach about the future estimation of the number of occupational accidents. Furthermore, through the comparison of numerical results from both models, the study demonstrates that national safety policies, particularly those enhancing the efficacy of OHS training, can effectively mitigate accidents.
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    Application of Reservoir Computers for Chaos Synchronization and Cracking Chaos-Based Cryptography in Fermionic 2D Thirring and 4D Gursey Models with Spinor Fields
    (World Scientific Publ Co Pte Ltd, 2025) Oniz, Yesim; Tosyali, Eren; Aydogmus, Fatma
    Reservoir computers have recently become one of the most widely exploited model-free approaches to chaos synchronization due to their fast convergence speed and simple yet effective learning rules. In this study, reservoir computing has been utilized to emulate the dynamics of chaotic Thirring and Gursey systems. In the supervised learning of the reservoir, one-step ahead states of the dynamical systems have been employed as the teaching signals. After the training phase, the reservoir was first run autonomously and then weakly driven by chaotic systems. It has been shown that the trained reservoir computers can exhibit the same characteristics as the attractors of the learned chaotic systems, which enable their use in synchronization tasks of chaotic systems with possible application in cracking chaos-based cryptography. To investigate the effect of noise on the performance of reservoir computers, noise signals with different colors and amplitudes have been included in the transmitted signals. The obtained results indicate that the proposed scheme can provide lower error metrics for both models.
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    Forecasting occupational accidents in Turkey using multivariate ARMAX and NLARX models
    (Nature Portfolio, 2026) Kaplanvural, Selcan; Tosyali, Eren; Ekmekci, Ismail
    Occupational accidents remain a critical issue in Turkey, with significant social and economic consequences, and understanding accident trends is essential for developing effective prevention strategies. This study employed both linear AutoRegressive Moving Average with Exogenous Input (ARMAX) and Nonlinear AutoRegressive with Exogenous Input (NLARX) models to forecast future occupational accidents using four accident-related populations (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_1$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_2$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_3$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_4$$\end{document}) derived from official insurance records. Due to the lack of consistently reported monthly data from the Social Security Institution (SSI), exogenous variables such as sectoral, economic, or demographic indicators were not incorporated, and the models were therefore identified based solely on the endogenous accident dynamics. The ARMAX identification process yielded a relatively large set of candidate parameters, which were subsequently evaluated using statistical significance criteria; only coefficients with p values below 0.05 and confidence intervals excluding zero were retained for interpretation. Model performance was evaluated using the normalized mean squared error (NMSE), which was computed separately for the training period, the test (out-of-sample forecasting) period, and the full dataset for each model. This multi-level evaluation enabled a consistent comparison of in-sample fitting accuracy, out-of-sample generalization capability, and overall predictive performance across ARMAX and NLARX models. The significance-based analysis revealed distinct linear dynamic structures across the output groups, with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(y_1,y_2)$$\end{document} populations characterized by a larger number of moderate-magnitude significant coefficients, whereas \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(y_3,y_4)$$\end{document} exhibited fewer but more dominant linear effects. The ARMAX model produced the lowest NMSE values across the training, test, and full datasets for most populations, demonstrating particularly strong and stable predictive accuracy for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_1$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_2$$\end{document}. The NLARX model yielded the best performance for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_1$$\end{document} and showed comparable NMSE values to ARMAX for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_2$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_4$$\end{document}, although it exhibited higher forecasting errors for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_3$$\end{document}, especially in the test period. Overall, the results indicated that while NLARX was capable of capturing nonlinear patterns in specific cases, the ARMAX framework provided a more robust, interpretable, and consistently generalizable representation of the dominant temporal dynamics governing occupational accident trends. These findings highlighted the potential of multivariate time series models to support evidence-based decision-making in occupational safety planning and policy development.
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    Master-slave synchronization in a 4D dissipative nonlinear fermionic system
    (Taylor & Francis Ltd, 2022) Aydogmus, Fatma; Tosyali, Eren
    It is known that the two controlled chaotic systems approach synchronization for any initial condition by proper controller design. Quite a number of alternative methods are available to synchronize the chaotic systems. Master-slave control technique is the most synchronization approaches used for the chaotic systems. In this paper, nonlinear active controller is obtained to synchronize the two identical dissipative fermionic systems in their chaotic states for different initial values. The synchronization is presented in the master-slave structure which implies that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. Also the numerical simulations are given to show the effectiveness of the used controllers.
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    Numerical Analysis of Thirring Model under White Noise
    (Iop Publishing Ltd, 2015) Aydogmus, Fatma; Tosyali, Eren
    Today, the effects of noise on dynamical systems are an attractive area of research. The noise acts as a driving term in the equations of motion in nonlinear systems. In this work, we present conformally invariant pure spin or nonlinear Thirring model. Thirring model describes Dirac fermions in (1+1) space-time dimensions with local current-current interaction. This model has rich dynamic of the quantization of relativistic quantum field theories. We investigate the response of Thirring oscillator to white noise by constructing phase space displays.
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    Regular and chaotic solutions in BEC for tilted bichromatical optical lattice
    (World Scientific Publ Co Pte Ltd, 2018) Tosyali, Eren; Aydogmus, Fatma; Yilmaz, Ayberk
    We investigate a Bose-Einstein condensate held in a 1D tilted bichromatical optical lattice potential by constructing its Poincare sections in phase space. We explore dynamic of the system based on the relations between the system parameters and the solution behaviors. It is demonstrated that the system exhibits shock-wave like dynamic. The power spectrum graphs, bifurcation and Lyapunov exponents of BEC system are also presented.
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    Shock Waves in Bose-Einstein Condensation Under Gaussian White Noise
    (World Scientific Publ Co Pte Ltd, 2018) Tosyali, Eren
    We investigate the Gross-Pitaevskii equation with the tilted bichromatical optical lattice potential for finding the dynamics of a Bose-Einstein condensate system under the Gaussian white noise. We construct the Poincare sections of system based on the relations between the system parameters and solution behaviors to understand how its shock wave like dynamic could be affected by the noise. Also the hierarchical cluster analysis method investigation of the system is presented.
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    Soliton Solutions of Gursey Model with Bichromatic Force
    (Amer Inst Physics, 2019) Tosyali, Eren; Aydogmus, Fatma
    Gursey proposed a spinor field equation which is similar to Heisenberg's nonlinear generalization of Dirac's equation. This equation is the first nonlinear conformal invariant wave equation. In this paper, we investigate the soliton solutions in Gursey wave equation held in a tilted bichromatic force by constructing their Poincare sections in phase space depending on the system parameters.