Skip to main content
Log in

Active systems with Nambu dynamics: with applications to rod wielding for haptic length perception and self-propagating systems on two-spheres

  • Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We generalize Nambu dynamics to describe self-excited, active systems that evolve on attractors and account for the up-take of energy and activation processes, on the one hand, and damping and inhibitory processes, on the other. An application to rod wielding for haptic length perception and a model for self-propagating systems on two-spheres are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • V.I. Arnold, Mathematical methods of classical mechanics (Springer, Berlin, 1978)

  • A. Isihara, Statistical physics (Academic Press, New York, 1971)

  • Y. Nambu, Phys. Rev. D 7, 2405 (1973)

    Google Scholar 

  • L. Takhtajan, Commun. Math. Phys. 160, 295 (1994)

    Google Scholar 

  • Y. Nutku, J. Phys. A 36, 7559 (2003)

  • A. Tegmen, Czech. J. Phys. 54, 749 (2004)

    Google Scholar 

  • S.A. Pandit, A.D. Gangal, J. Phys. A 31, 2899 (1998)

    Google Scholar 

  • T.L. Curtright, C. Zachos, New J. Phys. 4, 831 (2002)

  • T.L. Curtright, C. Zachos, Phys. Rev. D 68, 085001 (2002)

    Google Scholar 

  • C. Zachos, Phys. Lett. B 570, 82 (2003)

    Google Scholar 

  • D. Baleanu, Proc. Inst. Math. NAS of Ukraine 50, 611 (2004)

  • N.G. Pletnev, Siberian Electronic Mathematical Reports 6, 272 (2009)

  • M. Hirayama, Phys. Rev. D 16, 530 (1977)

    Google Scholar 

  • C. Gonera, Y. Nuktu, Phys. Lett. A 285, 301 (2001)

    Google Scholar 

  • A. Tegmen, A. Vercin, Int. J. Mod. Physics A 19, 393 (2004)

  • O. Babelon, D. Bernard, M. Talon, Introduction to classical integrable systems (Cambridge University Press, Cambridge, 2003)

  • U. Erdmann, W. Ebeling, L. Schimansky-Geier, F. Schweitzer, Eur. Phys. J. B 15, 105 (2000)

  • L. Schimansky-Geier, W. Ebeling, U. Erdmann, Acta Phys. Pol. B 36, 1757 (2005)

    Google Scholar 

  • U. Erdmann, W. Ebeling, Int. J. Bif. Chaos 15, 3623 (2005)

  • B. Lindner, E.M. Nicola, Eur. Phys. J. ST 157, 43 (2008)

  • J.W. Rayleigh, Theory of sound (Dover, New York, 1945), first edition published 1894

  • F. Verhulst, Nonlinear differential equations and dynamical systems, 2nd edn. (Springer, Berlin, 1996)

  • B.A. Kay, J.A.S. Kelso, E.L. Saltzman, G. Schöner, J. Exp. Psychol. Hum. Percept. Perform. 13, 178 (1987)

    Google Scholar 

  • B.A. Kay, E.L. Saltzman, J.A.S. Kelso, J. Exp. Psychol. Hum. Percept. Perform. 17, 183 (1987)

  • P.J. Beek, R.C. Schmidt, A.W. Morris, M. Sim, M.T. Turvey, Biol. Cybern. 73, 499 (1995)

    Google Scholar 

  • P.J. Beek, W.E.I. Rikkert, P.C.W. van Wieringen, J. Exp. Psychol. Hum. Percept. Perform. 22, 1077 (1996)

    Google Scholar 

  • P. Silva, M. Moreno, S. Fonseca, M.T. Turvey, Neurosci. Lett. 429, 64 (2009)

    Google Scholar 

  • F. Schweitzer, W. Ebeling, B. Tilch, Phys. Rev. Lett. 80, 5044 (1998)

    Google Scholar 

  • F. Schweitzer, Brownian agents and active particles (Springer, Berlin, 2003)

  • U. Erdmann, W. Ebeling, Fluc. Noise Lett. 2, L145 (2003)

  • F. Schweitzer, W. Ebeling, B. Tilch, Phys. Rev. E 64, 021110 (2001)

    Google Scholar 

  • U. Erdmann, W. Ebeling, A. Mikhailov, Phys. Rev. E 71, 051904 (2005)

    Google Scholar 

  • W. Ebeling, L. Schimansky-Geier, Eur. Phys. J. ST 157, 17 (2008)

  • F. Schweitzer, L. Schimansky-Geier, Physica A 206, 359 (1994)

    Google Scholar 

  • L. Schimansky-Geier, M. Meith, H. Rose, H. Malchow, Phys. Lett. A 207, 140 (1995)

  • A. Czirok, A.L. Barabasi, T. Vicsek, Phys. Rev. Lett. 82, 209 (1999)

    Google Scholar 

  • A. Czirok, T. Vicsek, Physica A 281, 17 (2000)

    Google Scholar 

  • H. Haken, Z. Physik 263, 267 (1973)

  • R. Graham, in Quantum statistics in optics and solid-state physics. Springer tracts in modern physics, Vol. 66, edited by G. Höhler (Springer, Berlin, 1973), pp. 1–97

  • M. Hongler, D.M. Ryter, Z. Physik B 31, 333 (1978)

    Google Scholar 

  • R. Feistel, W. Ebeling, Evolution of complex system: self-organization, entropy and development (VEB Verlag, Berlin, 1989)

  • W. Ebeling, I.M. Sokolov, Statistical thermodynamics and stochastic theory of nonequilibrium systems (World Scientific, Singapore, 2004)

  • W. Ebeling, Condens. Matt. Physics 3, 285 (2000)

    Google Scholar 

  • V.A. Makarov, W. Ebeling, M.G. Velarde, Int. J. Bif. Chaos 10, 1075 (2000)

    Google Scholar 

  • H.U. Bödeker, T.D. Frank, R. Friedrich, H.G. Purwins, in Anomalous fluctuation phenomena in complex systems: plasmas, fluids and financial markets, edited by C. Riccardi, H.E. Roman (Research Signpost, Kerala, 2008), pp. 145–184

  • T.D. Frank, D. Dotov, M.T. Turvey, A canonical-dissipative approach to control and coordination in the complex system called the agent-task-environment, submitted

  • T.D. Frank, On a moment-based data analysis method for canonical-dissipative oscillatory systems, Fluc. Noise Lett., in press

  • T.D. Frank, A. Daffertshofer, Physica A 292, 392 (2001)

  • T.D. Frank, Phys. Lett. A 319, 173 (2003)

  • T.D. Frank, Phys. Lett. A 337, 224 (2005)

  • T.D. Frank, Nonlinear Fokker-Planck equations: Fundamentals and applications (Springer, Berlin, 2005)

  • J. LaSalle, S. Lefschetz, Stability by Lyapunov's direct method (Academic Press, New York, 1961)

  • N. Goldenfeld, Sensation and perception (Wadsworth, Pacific Grove, CA, 2002)

  • H.Y. Solomon, M.T. Turvey, J. Exp. Psychol. Hum. Percept. Perform. 14, 404 (1988)

    Google Scholar 

  • H.Y. Solomon, M.T. Turvey, G. Burton, J. Exp. Psychol. Hum. Percept. Perform. 15, 58 (1989)

    Google Scholar 

  • C.C. Pagano, J.M. Kinsella-Shaw, P.E. Cassidy, M.T. Turvey, J. Exp. Psychol. Hum. Percept. Perform. 20, 276 (1994)

  • C.C. Pagano, K.C. Donahue, Percept. Psychophys. 61, 1336 (1999)

  • P. Fitzpatrick, C. Carello, M.T. Turvey, Neuroscience 60, 551 (1994)

    Google Scholar 

  • M.T. Turvey, G. Burton, E.L. Amazeen, M. Butwill, C. Carello, J. Exp. Psychol. Hum. Percept. Perform. 24, 35 (1998)

    Google Scholar 

  • C. Carello, P. Fitzpatrick, I. Flascher, M.T. Turvey, Percept. Psychophys. 60, 89 (1998)

    Google Scholar 

  • C. Neumann, Crelle Journal 56, 46 (1859)

  • A. Ramsey, Dynamics, Part II (Cambridge University Press, London, 1937)

  • A.R. Plastino, A. Plastino, Physica A 232, 458 (1996)

    Google Scholar 

  • G.B. Roston, A.R. Plastino, M. Casas, A. Plastino, L.R. da Silva, Eur. Phys. J. B 48, 87 (2005)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. D. Frank.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frank, T. Active systems with Nambu dynamics: with applications to rod wielding for haptic length perception and self-propagating systems on two-spheres. Eur. Phys. J. B 74, 195–203 (2010). https://doi.org/10.1140/epjb/e2010-00083-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2010-00083-8

Keywords

Navigation