Transport control in a deterministic ratchet system.

@article{Son2008TransportCI,
  title={Transport control in a deterministic ratchet system.},
  author={Woo-Sik Son and Jung-Wan Ryu and Dong-Uk Hwang and Soo-Young Lee and Young-Jai Park and Chil-Min Kim},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={77 6 Pt 2},
  pages={
          066213
        }
}
  • Woo-Sik Son, J. Ryu, Chil-Min Kim
  • Published 17 December 2006
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We study the control of transport properties in a deterministic inertia ratchet system via the extended delay feedback method. A chaotic current of a deterministic inertia ratchet system is controlled to a regular current by stabilizing unstable periodic orbits embedded in a chaotic attractor of the unperturbed system. By selecting an unstable periodic orbit, which has a desired transport property, and stabilizing it via the extended delay feedback method, we can control transport properties of… 
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References

SHOWING 1-10 OF 65 REFERENCES
Control of a Deterministic Inertia Ratchet System via Extended Delay Feedback
(Received 15 August 2006)We study the control of a transport property in a deterministic inertia ratchet system via ex-tended delay feedback. We stabilize a chaotic current of a ratchet system to a
Chaotic transport and current reversal in deterministic ratchets
  • Mateos
  • Physics
    Physical review letters
  • 2000
TLDR
The origin of the current reversal is identified as a bifurcation from a chaotic to a periodic regime, and trajectories revealing intermittent chaos and anomalous deterministic diffusion are observed.
Analytical properties and optimization of time-delayed feedback control.
  • Kestutis Pyragas
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
TLDR
It is shown that the main stability properties of the system controlled by time-delayed feedback can be simply derived from a leading Floquet exponent defining the system behavior under proportional feedback control.
Regular and chaotic transport in asymmetric periodic potentials: Inertia ratchets.
TLDR
This work characterizes the motion by cumulants of the contracted, time-dependent solution of the Liouville equation, and can distinguish regular from chaotic transport.
Anticipated synchronization in coupled inertial ratchets with time-delayed feedback: a numerical study.
TLDR
It is found that the slave ratchet can respond in exactly the same way as the master will respond in the future, thereby anticipating the nonlinear directed transport.
Control of chaos via an unstable delayed feedback controller.
TLDR
A modified scheme based on an unstable delayed feedback controller for stabilizing unstable periodic orbits embedded in chaotic attractors and shows efficiency for an unstable fixed point of a simple dynamic model and an unstable periodic orbit of the Lorenz system.
Deterministic directed transport of inertial particles in a flashing ratchet potential.
TLDR
It is shown that a critical threshold of the ratchet asymmetry is required for the system to achieve a net current and directed transport can be greatly enhanced when the coupling strength of particles is increased.
Directed chaotic transport in Hamiltonian ratchets.
TLDR
It is shown that regular ratchet transport can be directed against an external potential gradient while chaotic ballistic transport is restricted to unbiased systems.
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