## Generalized Form of Parrondo's Paradoxical Game with Applications to Chaos Control

- Marius-F. Danca, Michal Feckan, Miguel Romera
- I. J. Bifurcation and Chaos
- 2014

1 Excerpt

- Published 2003 in Physical review letters

We develop an analytically solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations, we obtain the steady-state probabilities. Generally, the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space, we find the null curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force.

@article{Lee2003MinimalBR,
title={Minimal Brownian ratchet: an exactly solvable model.},
author={Youngki Lee and Andrew Allison and Derek Abbott and Harry Eugene Stanley},
journal={Physical review letters},
year={2003},
volume={91 22},
pages={220601}
}