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Öğe 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, FatmaReservoir 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.Öğe Chaotic Dynamics and Analysis with Artificial Neural Networks of Aftershocks of 2019 Silivri Earthquake(2024) Aydogmus, Fatma; Oniz, Yesim; Simuratli, Eljan; Tosyalı, Eren; Kaplanvural, Ismaıl; Mutlu, Ahu Kömeç; Önem, Zeynep ÇiçekEarthquakes, whose physical, economic, psychological, and social damages can last for many years, are of vital importance for Türkiye, which is located in the most active earthquake zone that causes many earthquakes in the world. The North Anatolian Fault (NAF) is one of Türkiye's most important tectonic elements as it is the world’s fastest-moving right-lateral and strike-slip active fault zone consisting of many segments. The recent 5.8 magnitude 2019 Silivri earthquake, which occurred in the part of the NAF zone crossing the Marmara Sea, is an indicator that earthquake activity continues in the region. Aftershocks play a crucial role in seismicity research and seismic hazard assessments in terms of providing data and usable information in the examination of seismic dynamics with the changes observed in their time-dependent behavior and regional distribution. In this study, the aftershocks of the Silivri earthquake were examined as a natural laboratory using nonlinear analysis methods. Within the scope of the study, aftershocks of the Silivri earthquake were analyzed with a hybrid artificial neural network as well as different neural network structures, and for this purpose, data from 361 aftershocks with a magnitude greater than 1.5 in the year following the earthquake were used.Öğe Chaotic Dynamics and Analysis with Artificial Neural Networks of Aftershocks of 2019 Silivri Earthquake(Gazi University, 2024) Aydogmus, Fatma; Öniz, Yeşim; Simuratli, Eljan; Tosyalı, Eren; Kaplanvural, İsmail; Mutlu, Ahu Kömeç; Çaka, DenizEarthquakes, whose physical, economic, psychological, and social damages can last for many years, are of vital importance for Türkiye, which is located in the most active earthquake zone that causes many earthquakes in the world. The North Anatolian Fault (NAF) is one of Türkiye's most important tectonic elements as it is the world’s fastest-moving right-lateral and strike-slip active fault zone consisting of many segments. The recent 5.8 magnitude 2019 Silivri earthquake, which occurred in the part of the NAF zone crossing the Marmara Sea, is an indicator that earthquake activity continues in the region. Aftershocks play a crucial role in seismicity research and seismic hazard assessments in terms of providing data and usable information in the examination of seismic dynamics with the changes observed in their time-dependent behavior and regional distribution. In this study, the aftershocks of the Silivri earthquake were examined as a natural laboratory using nonlinear analysis methods. Within the scope of the study, aftershocks of the Silivri earthquake were analyzed with a hybrid artificial neural network as well as different neural network structures, and for this purpose, data from 361 aftershocks with a magnitude greater than 1.5 in the year following the earthquake were used.Öğe Master-slave synchronization in a 4D dissipative nonlinear fermionic system(Taylor & Francis Ltd, 2022) Aydogmus, Fatma; Tosyali, ErenIt 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.Öğe Numerical Analysis of Thirring Model under White Noise(Iop Publishing Ltd, 2015) Aydogmus, Fatma; Tosyali, ErenToday, 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.Öğe Regular and chaotic solutions in BEC for tilted bichromatical optical lattice(World Scientific Publ Co Pte Ltd, 2018) Tosyali, Eren; Aydogmus, Fatma; Yilmaz, AyberkWe 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.Öğe Soliton Solutions of Gursey Model with Bichromatic Force(Amer Inst Physics, 2019) Tosyali, Eren; Aydogmus, FatmaGursey 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.Öğe Synchronization of Gursey System(2022) Tosyalı, Eren; Aydogmus, FatmaGursey Model, the only possible four-dimensional pure spinor model, proposed as a possible basis for a unitary description of elementary particles. The model exhibits chaotic behaviors depending on the system parameter values. In this study, we investigate the synchronization of chaotic dynamic in the Gursey wave equation that has particle-like solutions derived classical field equations. Numerical results for synchronization of the Gursey system are performed to indicate the accuracy of the used method.
