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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.