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    Analysis of patterns in an additional food-provided predator-prey reaction diffusion model using amplitude equations
    (Indian Acad Sciences, 2023) Ghorai, Santu; Umut, Omur; Poria, Swarup
    A two-species predator-prey reaction diffusion model where additional food was provided to the predator has been considered in the presence of both self- and cross-diffusion terms in a two-dimensional space. Importance of self- and cross-diffusion terms are discussed ecologically. Linear stability analysis has been done to determine the Turing instability region of the parameter space. Impacts of the cross-diffusion term on the stability behaviour are discussed. Using weak nonlinear analysis, the amplitude equations has been formulated to predict the stability of hexagonal, stripes and their mixture patterns near the Turing thresholds analytically. Finite difference method has been used for numerical simulations of the model under no-flux boundary conditions. Numerical simulation results are in good agreement with the theoretical predictions of patterns near the Turing threshold using amplitude equations. Additional food can play a significant role in pattern forming instabilities because near the Turing thresholds small fluctuation of additional food parameter can produce a wide variety of Turing patterns.
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    CHAOS CONTROL IN GENESIO SYSTEM USING ACTIVE BACKSTEPPING DESIGN
    (Taylor & Francis Ltd, 2010) Umut, Omur
    In this paper, an active backstepping design is proposed for controlling chaotic Genesio system to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. This method is also applied to achieve chaos synchronization of two identical Genesio system with each other. The proposed method, which is based on Lyapunov stability theorem, combines active control and backstepping methods. Numerical simulations verify the effectiveness and feasibility of the method.
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    CHAOS SYNCHRONIZATION
    (Taylor & Francis Ltd, 2007) Umut, Omur; Poria, Swarup; Patra, Rajat
    In this paper, we use nonlinear control method for synchronization of two identical chaotic generalized Lotka-Volterra system. The determination of the controller is based on the Lyapunov stability theory. Numerical simulation results are shown for demonstration.
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    CHAOS SYNCHRONIZATION OF LU DYNAMICAL SYSTEM VIA LINEAR TRANSFORMATIONS
    (Taylor & Francis Ltd, 2006) Poria, Swarup; Umut, Omur
    Generalized synchronization of two unidirectionally coupled dynamical systems is a generalization of identical synchronization. In this paper, we study a special case of generalized synchronization e.g., linear generalized synchronization of two Lu dynamical systems.