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    Chaos synchronization of genesio system
    (World Scientific Publ Co Pte Ltd, 2009) Umut, Ömür
    This paper presents chaos synchronization of two identical Genesio systems by using three methods; Pecora and Carroll, active control and linear generalized synchronization. We demonstrate that coupled Genesio systems call be synchronized. Numerical simulations are given to verify the effectiveness of these methods.
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    Controlling chaos in nuclear spin generator system using backstepping design
    (2009) Umut, Ömür
    In the present paper backstepping design is proposed to control nuclear spin generator system based on parameters identification. The observer is designed to identify the unknown parameter of NSG system. And on this basis, an efficient backstepping design is developed for controlling the uncertain NSG system to bounded points and tracking any desired trajectory. Numerical simulations are provided to show the effectiveness and feasibility of the proposed method. © Balkan Society of Geometers, Geometry Balkan Press 2009.
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    Generalized synchronization of nuclear spin generator system
    (2008) Molaei M.R.; Umut, Ömür
    Synchronization of chaotic oscillators in a generalized sense leads to richer behavior than identical chaotic oscillations in coupled systems. In this paper, we study the generalized synchronization of uni-directionally coupled nuclear spin generator system. © 2006 Elsevier Ltd. All rights reserved.
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    Relative probability synchronization for dynamical systems created by homeomorphisms
    (2010) Molaei, Mohammad Reza; Umut, Ömür
    In this paper, using the relative probability measure, the notion of synchronized dynamical systems from the viewpoint of an observer for discrete topological dynamical systems created by the homeomorphisms of a metric space, is considered. A kind of equivalence relation up to the suitable observers, is deduced. It is proved that: topological conjugacy implies to the relative probability synchronization. The notion of relative probability synchronization for the ideal observers on the probability spaces, is studied. The relative probability synchronization of the time one maps of the solutions of Chua's diode and its driven system by the different observers, are studied. © 2010 Institute of Advanced Scientific Research.
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    Routh-hurwitz conditions and lyapunov second method for a nonlinear system
    (World Scientific Publ Co Pte Ltd, 2010) Umut, Ömür
    In this paper, a Lyapunov function is generated to determine the domain of asymptotic stability of a system of three first order nonlinear ordinary differential equations describing the behaviour of a nuclear spin generator (NSG) The generated Lyapunov function, is a. simple quadratic form: whose coefficients am chosen so that the Routh-Hurwitz criteria are satisfied for the corresponding linear differential equations