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Journal of Chaos    Follow    
  This is an Open Access Journal Open Access journal
     ISSN (Online) 2314-6605
     Published by Hindawi Publishing Corporation Homepage  [347 journals]
  • Reduced Order Projective and Hybrid Projective Combination-Combination
           Synchronization of Four Chaotic Josephson Junctions
    • Abstract: This paper investigates the reduced order projective and hybrid projective combination-combination synchronization of four chaotic Josephson junctions consisting of two third order Josephson junctions as the drives and two second order chaotic Josephson junctions as the response systems via active backstepping technique. The investigation confirms the achievement of reduced order projective and hybrid projective combination-combination synchronization among four chaotic Josephson junctions via active backstepping technique. Numerical simulations are validated to show the effectiveness of the synchronization scheme. Reduced order combination-combination synchronization scheme has more significant applications to neural encoding and decoding of information in biological systems and to the security of information transmission in communication systems than the usual one drive system and one response system synchronization scheme.
      PubDate: Thu, 13 Feb 2014 16:10:44 +000
  • Synchronization and Stabilization of Chaotic Dynamics in a Quasi-1D
           Bose-Einstein Condensate
    • Abstract: A nonlinear control is proposed for the exponential stabilization and synchronization of chaotic behaviour in a model of Bose-Einstein condensate (BEC). The active control technique is designed based on Lyapunov stability theory and Routh-Hurwitz criteria. The control design approach in both cases guarantees the stability of the controlled states. Whereas the synchronization of two identical BEC in their chaotic states can be realized using the scheme; a suitable controller is also capable of driving the otherwise chaotic oscillation to a stable state which could be expected in practice. The effectiveness of this technique is theoretically and numerically demonstrated.
      PubDate: Thu, 12 Dec 2013 14:07:06 +000
  • Dynamical Properties and Finite-Time Hybrid Projective Synchronization
           Using Fractional Nonsingular Sliding Mode Surface in Fractional-Order
           Two-Stage Colpitts Oscillators
    • Abstract: The dynamics and robust finite-time hybrid projective synchronization of a fractional-order four-dimensional nonlinear system based on a two-stage Colpitts oscillator is investigated. The study of the fractional order stability of the equilibrium states of the system is carried out. The bifurcation diagram confirms the occurrence of Hopf bifurcation in the proposed system when the fractional-order passes a sequence of critical values; the Lyapunov exponent shows the different chaotic sequences of the system. Further, a fractional nonsingular terminal sliding surface and an appropriate robust fractional sliding mode control law are proposed for the finite-time hybrid projective synchronization of a fractional-order chaotic two-stage Colpitts oscillator by taking into account the effects of model uncertainties and the external disturbances. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. Finally, some numerical simulations are presented to demonstrate the effectiveness and applicability of the proposed technique.
      PubDate: Wed, 11 Dec 2013 13:54:14 +000
  • On a New Cournot Duopoly Game
    • Abstract: This paper presents a new Cournot duopoly game. The main advantage of this game is that the outputs are nonnegative for all times. We investigate the complexity of the corresponding dynamical behaviors of the game such as stability and bifurcations. Computer simulations will be used to confirm our theoretical results. It is found that the chaotic behavior of the game has been stabilized on the Nash equilibrium point by using delay feedback control method.
      PubDate: Mon, 30 Sep 2013 10:51:38 +000
  • Synchronization of Uncertain Fractional-Order Hyperchaotic Systems via
           Unidirectional Linear Error Feedback Coupling Scheme
    • Abstract: A simple method for synchronization of uncertain fractional-order hyperchaotic systems is proposed in this paper. The method makes use of a unidirectional linear coupling approach due to its simple configuration and ease of implementation. To determine the coupling parameters, the synchronization error dynamics is first formulated as a fractional-order linear interval system. Then, the parameters are obtained by solving a linear matrix inequality (LMI) stability condition for stabilization of fractional-order linear interval systems. Thanks to the existence of an LMI solution, the convergence of the synchronization errors is guaranteed. The effectiveness of the proposed method is numerically illustrated by the uncertain fractional-order hyperchaotic Lorenz system.
      PubDate: Wed, 18 Sep 2013 11:55:23 +000
  • Finite-Time Combination-Combination Synchronization for Hyperchaotic
    • Abstract: A new type of finite-time synchronization with two drive systems and two response systems is presented. Based on the finite-time stability theory, step-by-step control and nonlinear control method, a suitable controller is designed to achieve finite-time combination-combination synchronization among four hyperchaotic systems. Numerical simulations are shown to verify the feasibility and effectiveness of the proposed control technique.
      PubDate: Sun, 01 Sep 2013 09:45:22 +000
  • Control of Chaos in Rate-Dependent Friction-Induced Vibration Using
           Adaptive Sliding Mode Control and Impulse Damper
    • Abstract: Two different control methods, namely, adaptive sliding mode control and impulse damper, are used to control the chaotic vibration of a block on a belt system due to the rate-dependent friction. In the first method, using the sliding mode control technique and based on the Lyapunov stability theory, a sliding surface is determined, and an adaptive control law is established which stabilizes the chaotic response of the system. In the second control method, the vibration of this system is controlled by an impulse damper. In this method, an impulsive force is applied to the system by expanding and contracting the PZT stack according to efficient control law. Numerical simulations demonstrate the effectiveness of both methods in controlling the chaotic vibration of the system. It is shown that the settling time of the controlled system using impulse damper is less than that one controlled by adaptive sliding mode control; however, it needs more control effort.
      PubDate: Sun, 21 Jul 2013 10:32:13 +000
  • Difficulties in Evaluating Lyapunov Exponents for Lie Governed Dynamics
    • Abstract: We consider here an environment in which the fact that a semiquantum Hamiltonian obeys SU(2) symmetries poses serious difficulties if one wants to compute Lyapunov exponents.
      PubDate: Thu, 11 Jul 2013 13:51:09 +000
  • Unstable Manifolds of Continuous Self-Mappings
    • Abstract: Unstable manifolds of continuous self-mappings on completely densely ordered linear ordered topological spaces (CDOLOTS) are discussed. Let be a continuous self-map. First, the interval with endpoints of two adjacent fixed points is contained in the unilateral unstable manifold of one of the endpoints. Then, by using the above conclusion, we prove that periodic points of not belong to the unstable manifold of their iteration points of (for some ), unless the iteration points are themselves.
      PubDate: Wed, 05 Jun 2013 18:04:36 +000
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