Synchronization, anti-synchronization and current transports in non-identical chaotic ratchets

Vincent, U. E.; Laoye, J. A.

doi:10.1016/j.physa.2007.05.044

Cited by 44 publications

(27 citation statements)

References 42 publications

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“…Nonlinear anti-synchronization controllers for nonlinear gyros and non-identical chaotic ratchets were proposed in [6] and [7], respectively. Recently, Al-sawalha and Noorania [8] constructed nonlinear controllers for anti-synchronization between two identical and different chaotic systems.…”

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confidence: 99%

Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control

Ahn¹

2009

Int J Theor Phys

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This paper investigates the adaptive anti-synchronization problem for timedelayed chaotic neural networks with unknown parameters. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) approach, the adaptive anti-synchronization controller is designed and an analytic expression of the controller with its adaptive laws of unknown parameters is shown. The proposed controller can be obtained by solving the LMI problem. An illustrative example is given to demonstrate the effectiveness of the proposed method.

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confidence: 99%

Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control

Ahn¹

2009

Int J Theor Phys

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“…It has been experimentally, as well as numerically confirmed, that the two coupled chaotic systems can achieve AS [16,17]. The AS phenomenon in non-equilibrium systems suggests that it can be used as a technique for particle separation in a mixture of interacting particles [17]. A current study of using AS control of lasers, one can generate not only drop-outs in intensity but also short high-intensity pulses, and this results in pulses of particular shapes [18].…”

Section: Introductionmentioning

confidence: 93%

“…AS has successful applications in different scientific disciplines [14,15]. It has been experimentally, as well as numerically confirmed, that the two coupled chaotic systems can achieve AS [16,17]. The AS phenomenon in non-equilibrium systems suggests that it can be used as a technique for particle separation in a mixture of interacting particles [17].…”

Section: Introductionmentioning

confidence: 99%

Robust Finite-Time Anti-Synchronization of Chaotic Systems with Different Dimensions

et al. 2015

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Abstract:In this paper, we demonstrate that anti-synchronization (AS) phenomena of chaotic systems with different dimensions can coexist in the finite-time with under the effect of both unknown model uncertainty and external disturbance. Based on the finite-time stability theory and using the master-slave system AS scheme, a generalized approach for the finite-time AS is proposed that guarantee the global stability of the closed-loop for reduced order and increased order AS in the finite time. Numerical simulation results further verify the robustness and effectiveness of the proposed finite-time reduced order and increased order AS schemes.

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“…The possible resultant effects have been considered in several different contexts [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. These studies have been motivated largely by the fact that many such systems, for example molecular motors, coexist in large numbers and do work in mutual cooperation [13].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the interplay between noise and coupling in a system of interacting particles is relevant for many applications [41][42][43][44]. The effect of noise on coupled inertia ratchets has hitherto been neglected [18][19][20][21][22][23][24][25][26][27][28]. Consideration of noise is also significant because interesting and potentially useful phenomena may emerge.…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

Vincent

Nana-Nbendjo

McClintock³

2013

Phys. Rev. E

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We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic.

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Synchronization, anti-synchronization and current transports in non-identical chaotic ratchets

Cited by 44 publications

References 42 publications

Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control

Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control

Robust Finite-Time Anti-Synchronization of Chaotic Systems with Different Dimensions

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

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