Exact ratchet description of Parrondo's games with self-transitions

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5471, Issue , 2004, Pages 407-415

  Amengual, Pau ^a   Toral, Raúl ^a  

^a INSTITUTO MEDITERRÁNEO DE ESTUDIOS AVANZADOS   (Spain)

Author keywords

Master and Fokker Planck equations; Multiplicative noise; Parrondo's games

Indexed keywords

MASTER AND FOKKER-PLANCK EQUATIONS; MULTIPLICATIVE NOISE; PARRANDO'S GAMES; SELF-TRANSITION;

INFORMATION THEORY; INTEGRATION; LARGE SCALE SYSTEMS; OPTIMAL CONTROL SYSTEMS; PROBABILITY; RANDOM PROCESSES; THERMAL DIFFUSION; THERMAL NOISE;

GAME THEORY;

EID: 4444276728     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.556418     Document Type: Conference Paper

References (24)

1. Harmer, G. P. & Abbott, D. 2002 A review of Parrondo's paradox. Fluctuation and Noise Letters 2, R71-R107.
2. Reimann, P. 2002 Brownian motors: noisy transport far from equilibrium. Physics Reports 361, 57-265.
3. Harmer, G. P. & Abbott, D. 1999 Parrondo's paradox. Statistical Science 14, 206-213.
4. Harmer, G. P. & Abbott, D. 1999b Losing strategies can win by Parrondo's paradox. Nature 402, 864.
5. Kay, R. J. & Johnson, N. F. 2002 Winning combinations of history-dependent games. Physical Review E 67, 056128(6).
6. Harmer, G. P., Abbott, D., & Taylor, P. G., Parrondo, J. M. R. 2001 Brownian ratchets and Parrondo's games. Chaos 11, 705-714.
7. C. Van den Broeck, P. Reimann, R. Kawai, P. Hänggi, Lect. Notes in Physics 527 (1999) 93.
8. Flitney, A. P., Xg, J. & Abbott, D. 2002 Quantum Parrondo's games. Physica A 314, 35-42.
9. Arena, P., Fazzino, S., Fortuna, L. & Maniscalco, P. 2003 Game theory and non-linear dynamics: the Parrondo paradox case study. Chaos, Solitons and Fractals 17, 545-555.
10. Toral, R. 2001 Cooperative Parrondo's games. Fluctuations and Noise Letters 1, L7-L12.
11. Toral, R. 2002 Capital redistribution brings wealth by Parrondo's paradox. Fluctuations and Noise Letters 2, L305-L311.
12. Kocarev, L. & Tasev, Z. 2002 Lyapunov exponents, noise-induced synchronization, and Parrondo's paradox. Physical Review E 65, 046215(4).
13. Dinis, L. & Parrondo, J. M. R. 2002 Parrondo's paradox and the risks of short-range optimization. Preprint cond-mat/0212358.
14. Buceta, J., Lindenberg, K. & Parrondo, J. M. R. 2002 Spatial patterns induced by random switching. Fluctuation and Noise Letters 2, L21-L29.
15. Buceta, J., Lindenberg, K. & Parrondo, J. M. R. 2002 Pattern formation induced by nonequilibrium global alternation of dynamics. Physical Review E 66, 036216(11).
16. Buceta, J. & Lindenberg, K. 2002 Switching-induced Turing instability. Physical Review E 66, 046202(4).
17. Ait-Haddou, R. & Herzog, W. 2002 Force and motion generation of myosin motors: muscle contraction. J. Electromyography and Kinesiology 12, 435-445.
18. Heath, D., Kinderlehrer, D. & Kowalczyk, M. 2002 Discrete and continuous ratchets: from coin toss to molecular motor. Discrete and Continuous Dynamical Systems-Series B 2, 153-167.
19. Boman, M., Johansson, S. J. & Lyback, D. 2001 Parrondo strategies for artificial traders. Intelligent Agent Technology (eds. N. Zhong, J. Liu, S. Ohsuga & J. Bradshaw), 150-159. World Scientific. Also available at cs/0204051.
20. Toral, R., Amengual, P. & Mangioni, S. 2003 Parrondo's games as a discrete ratchet. Physica A 327, 105-110.
21. Toral, R., Amengual, P. & Mangioni, S. 2003 A Fokker-Planck description for Parrondo's games. Proc. SPIE Noise in complex systems and stochastic dynamics (eds. L. Schimansky-Geier, D. Abbott, A. Neiman & C. Van den Broeck), 5114, 309-317. Santa Fe.
22. Allison, A., & Abbott, D. 2002 The physical basis for Parrondo's games. Fluctuation and Noise Letters 2, L327-L342.
23. Gardiner, C. W. 1994 Handbook of Stochastic Methods. Springer-Verlag. Berlin.
24. Amengual, P., Allison, A., Toral, R. & Abbott, D. 2004 Discrete-time ratchets, the Fokker-Planck equation and Parrondo's paradox. Accepted in Proc. R. Soc. London A.