Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H.G. Schuster, Deterministic chaos, 3rd augm. ed. (VCH, Weinheim, 1995).
E. Ott, Chaos in Dynamical Systems. (Cambridge University Press, Cambridge, 1993).
M. Mézard, G. Parisi, M.A. Virasoro, Spin glass theory and beyond (World Scientific, Singapore, 1987).
H. van Beijeren, J.R. Dorfman, Phys. Rev. Lett. 74, 4412 (1995); and refs. therein.
D. Weiss et al.: Phys. Rev. Lett. 66, 2790 (1991).
R. Fleischmann, T. Geisel, R. Ketzmerick, Phys. Rev. Lett. 68, 1367 (1992).
T. Geisel, J. Nierwetberg, Phys. Rev. Lett. 48, 7 (1982).
S. Grossmann, H. Fujisaka, Phys. Rev. A 26, 1779 (1982); H. Fujisaka, S. Grossmann, Z. Phys. B 48, 261 (1982).
M. Schell, S. Fraser, R. Kapral, Phys. Rev. A 26, 504 (1982).
R. Artuso, Phys. Lett. A 202, 195 (1992); G. Zumofen, J. Klafter, Phys. Rev. E 47, 851 (1993); X.-J. Wang, C.-K. Hu, Phys. Rev. E 48, 728 (1993); R. Artuso, G. Casati, R. Lombardi, Phys. Rev. Lett. 71, 62 (1993); R. Stoop, Phys. Rev. E 49, 4913 (1994); G. Radons, Phys. Rep. 290, 67 (1997).
T. Geisel, S. Thomae, Phys. Rev. Lett. 52, 1936 (1984).
R. Klages, J.R. Dorfman, Phys. Rev. Lett. 74, 387 (1995).
G. Radons, Phys. Rev. Lett. 77, 4748 (1996).
T. Geisel, J. Nierwetberg, A. Zacherl, Phys. Rev. Lett. 54, 616 (1985).
C. Beck, F. Schlögl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1993).
W. Just, On symbolic dynamics of spae-time chaotic models, in this book.
J.-P. Bouchaud, A. Georges, Phys. Rep. 195, 127 (1990).
Ya. G. Sinai, Theor. Prob. Appl. 27, 247 (1982).
A. Golosov, Commun. Math. Phys. 92, 491 (1984).
J. Chave, E. Guitter, J. Phys. A 32, 445 (1999).
C. Monthus, P. Le Doussal, Phys. Rev. E 65, 066129 (2002).
B.D. Hughes, Random Walks and Random Environments, Vol.2: Random Environments, Chap.6 (Clarendon Press, Oxford, 1996).
L. Lundgren et al., Phys. Rev. Lett. 51, 911 (1983).
L.C.E. Struik, Physical Aging in Amorphous Polymers and other Materials (Elsevier, Amsterdam, 1978).
M. Rubí, C. Pérez-Vicente (eds.), Complex Behaviour in Glassy Systems (Springer, Berlin, 1997).
J.P. Bouchaud, L.F. Cugliandulo, J. Kurchan, M. Mézard, in: A.P. Young (ed.), Spin Glasses and Random Fields (World Scientific, Singapore, 1998), cond-mat/9702070.
E. Vincent, et al., in: [25], p.184, cond-mat/9607224.
E. Marinari, G. Parisi, J. Phys. A 26, L1149 (1993).
F. Ritort, Phys. Rev. Lett. 75, 1190 (1995).
H. Horner, Glassy dynamics and aging in disordered systems, in this book.
L. Laloux, P. Le Doussal, Phys. Rev. E 57, 6296 (1998).
D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998).
P. Le Doussal, C. Monthus, D.S. Fisher, Phys. Rev. E 59, 4795 (1999).
G. Radons, Adv. Solid State Physics / Festkörperprobleme 38, 439 (1999).
L.F. Cugliandulo, J. Kurchan, G. Parisi: J.Phys. I France 4, 1641 (1994).
E. Barkai, Phys. Rev. Lett. 90, 104101 (2003).
J. Dräger, J. Klafter, Phys. Rev. Lett. 84, 5998 (2000).
J. Heldstab, H. Thomas, T. Geisel, G. Radons, Z. Phys. B 50, 141 (1983), S. Grossmann, Z. Phys. B 57, 77 (1984).
M. Bianucci, R. Manella, X. Fan, P. Grigolino, B.J. West, Phys. Rev. E 47, 1510 (1993), M. Bianucci, R. Manella, B.J. West, P. Grigolino, Phys. Rev. E 50, 2693 (1994).
P. Jung, J.G. Kissner, P. Hänggi, Phys. Rev. Lett. 76, 3436 (1996).
T. Harms, R. Lipowsky, Phys. Rev. Lett. 79, 2895 (1997).
B. Derrida, Y. Pomeau, Phys. Rev. Lett. 48, 627 (1982), B. Derrida, J. Stat. Phys. 31, 433 (1983).
E. Barkai, J. Klafter, Phys. Rev. Lett. 79, 2245 (1997).
S.N. Majumdar, A. Comtet, Phys. Rev. E 66, 061105 (2002).
C. Monthus, Localization properties of the anomalous diffusion phase x ∼ tμ in the directed trap model and in the Sinai diffusion with bias. cond-mat/0212212.
C. Monthus, P. Le Doussal, Energy dynamics in the Sinai model. cond-mat/0206035.
P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
E. Hopf, Ergodentheorie (Springer, Berlin, 1937).
G. Radons, J. Phys. A 31, 4141 (1998).
G. Radons, Physica D 187, 3 (2004).
E.S. Key, Ann. Probab. 12, 529 (1984).
J. Buck, E. Buck, Scientific American 234, 74 (1976).
S.H. Strogatz, I. Stewart, Scientific American 269, 102 (1993).
A.T. Winfree, J. Theoret. Biol. 16, 15 (1967).
R. Eckhorn, et al., Biol. Cybern. 60, 121 (1988).
A.K. Engel, et al., Eur. J. Neurosci. 2, 588 (1990).
K. Otsuka, Phys. Rev. Lett. 67, 1090 (1991).
K. Wiesenfeld, et al., Phys. Rev. Lett. 65, 1749 (1990).
Y. Kuramoto, Chemical oscillations, waves and turbulence (Springer, Berlin, 1984).
H. Daido, J. Phys. A 20, L629 (1987).
Y. Kuramoto, I. Nishikawa, J. Stat. Phys. 49, 569 (1987).
S.H. Strogatz, E. Mirollo, J. Stat. Phys. 63, 613 (1992).
W.F. Wreszinski, J.L. van Hemmen, J. Stat. Phys. 72, 145 (1993).
S.H. Strogatz, E. Mirollo, P.C. Matthews, Phys. Rev Lett. 68, 2730 (1992).
J.D. Crawford, J. Stat. Phys. 74, 1047 (1994), Phys. Rev Lett. 74, 4341 (1995).
L.L. Bonilla, C.J. Pérez Vicente, R. Spigler, Physica D 113, 79 (1998).
S.H. Strogatz, Physica D 143, 1 (2000).
A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization (Cambridge University Press, Cambridge, 2001).
M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions (Dover, New York, 1965).
H. Posch, C. Forster: Lyapunov nstability of fluids, in this book.
J.C. Stiller, G. Radons, Lyapunov Spectrum of the Kuramoto Model of Nonlinear Oscillators, preprint.
J.C. Stiller, Dynamik von Phasenoszillatoren, Diploma thesis, Kiel (1994).
H. Daido, Phys. Rev. Lett. 73, 760 (1994), Physica D 91, 24 (1996).
J.T. Ariaratnam, S.H. Strogatz, Phys. Rev Lett. 86, 4278 (2001).
H. Daido, Phys. Rev. Lett. 68, 1073 (1992).
P. Spitzner, W. Kinzel, Z. Phys. B. 77, 511 (1989).
J.C. Stiller, G. Radons, Phys. Phys. Rev. E 58, 1789 (1998), J. C. Stiller, G. Radons, Phys. Rev. E 61, 2148 (2000).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Radons, G. (2005). Disordered Dynamical Systems. In: Radons, G., Just, W., Häussler, P. (eds) Collective Dynamics of Nonlinear and Disordered Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26869-3_13
Download citation
DOI: https://doi.org/10.1007/3-540-26869-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21383-3
Online ISBN: 978-3-540-26869-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)