Dr Uchechukwu Vincent

In this Letter, we propose a single control input approach for stabilizing three-dimensional chaotic systems in a finite time. The method is more general and is derived from the finite-time stability theory and adaptive control technique; and can stabilize almost all well-known three-dimensional chaotic systems without a prior knowledge of the feedback gain. To show the wider applicability of our method, we give illustrations using different chaotic systems with different structure. Numerical simulations are also used to verify the effectiveness of the technique.

Keywords: Chaos; Chaos control; Finite time stabilization

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Controlling current reversals in synchronized underdamped ratchets

Published in J. Physics A: Mathematical and Theoretical 40(16), 165101 (2010)

A pair of underdamped ratchets, coupled via a perturbed asymmetric potential, is shown to make a transition to a fully synchronized state wherein stable controlled transport is achieved when the coupling strength exceeds a threshold at which the collective dynamics is attained. This transition to collective transport is connected to a chaos-periodic / quasiperiodic bifurcation in which current reversal is completely eliminated. Based on the Lyapunov stability theory and linear matrix inequalities, we give some necessary and sufficient criteria for stable controlled transport and obtain an exact analytic estimate of the threshold (kth) for the onset of stable controlled current.

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Current reversals and synchronization in coupled ratchets

Published in Physical Review E 82, 046208 (2010)

Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k_th, a specific driving amplitude a_opt is found for which the transport is optimum.

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Synchronization and control of directed transport in chaotic ratchets via active control

published in Phys. Lett. A 363 (2007) 91

Using a technique derived from nonlinear control theory, we demonstrate that two identical inertial ratchets transporting particles in two directions can be synchronized such that both ratchets transport particles in a desired direction. This novel approach to control of directed transport is applicable when there are multiple co-existing attractors in phase space transporting particles in different directions. Numerical simulations are employed to illustrate the approach

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Synchronization of chaos in RCL-shunted Josephson junction using a simple adaptive controller

Published in Physica Scripta 79, 035801 (2009)

In this paper, a simple adaptive control is proposed for the synchronization of chaotic dynamics of resistive–capacitive–inductive-shunted Josephson junctions (RCLSJ). The synchronization problem is investigated based on a drive–response system configuration consisting of two identical RCLSJ with and without identical system parameters. In addition, the synchronization when the system parameters are unknown is considered based on adaptive parameter control estimation. Sufficient conditions for global asymptotic synchronization are given and numerical simulations are employed to demonstrate the efficiency of the adaptive control scheme. In the presence of noise, we also show that the synchronization is robust and discuss the implication of our adaptive control technique in rapid single flux quantum (RSFQ) devices.

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Synchronization, multistability and basin crisis in coupled pendula

Published in Journal of Sound and Vibration 329 (2010) 443–456

The synchronization dynamics of two linearly coupled pendula is studied in this paper. Based on the Lyapunov stability theory and Linear matrix inequality (LMI); some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling kth, for the on-set of full synchronization is obtained. The numerical value of kth determined from the average energies of the systems is in good agreement with theoretical analysis. Prior to the on-set of synchronization, the boundary crisis of the chaotic attractor is identified. In the bistable states, where two asymmetric periodic attractors co-exist, it is shown that the coupled pendula can attain multistable states via a new dynamical transition—the basin crisis that occur prior to the on-set of stable synchronization. The essential feature of basin crisis is that the two co-existing attractors are destroyed while new three or more co-existing attractors of the same or different periodicity are created. In addition, the linear perturbation technique and the Routh–Hurwitz criteria are employed to investigate the stability of steady states, and clearly identify the different types of bifurcations likely to be encountered. Finally, two-parameter phase plots, show various regions of chaos, hyperchaos and periodicity.

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A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems

Published in Communications in Nonlinear Science and Numerical Simulations 14 (2009) 3925–3932

In this paper, a simple adaptive feedback control is proposed for full and reduced-order synchronization of time-varying and strictly uncertain chaotic systems. Our method uses only one feedback gain with parameter adaptation law and converges very fast even in the presence of noise. For full synchronization, a drive-response system consisting of two second-order identical parametrically excited oscillators achieve global synchronization;
while for reduced-order synchronization, the dynamical evolution of a second-order parametrically driven oscillator is synchronized with the projection of a third-order time-varying chaotic system. The effectiveness of our approach is demonstrated using numerical simulations.

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