Complutense University Library

Mode transitions and wave propagation in a driven-dissipative Toda-Rayleigh ring


Makarov, Valeri A. and Río, E. del and Velarde, Manuel G. and Ebeling, Werner (2003) Mode transitions and wave propagation in a driven-dissipative Toda-Rayleigh ring. Physical Review E, 67 (5). 056208-1. ISSN 1539-3755

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:


A circular lattice (ring) of N electronic elements with Toda-type exponential interactions and Rayleigh-type dissipation is used to illustrate wave formation, propagation, and switching between wave modes. A methodology is provided to help controlling modes, thus allowing it to realize any of (N-1) different wave modes (including soliton-type modes) and the switching between them by means of a single control parameter.

Item Type:Article
Uncontrolled Keywords:Map lattices; Gaits; Oscillators; Walking; Systems; Analog
Subjects:Sciences > Mathematics > Functions
ID Code:16868

E.R. Kandel, J.H. Schwartz, and T.M. Jessell, Principles of Neural Science, 4th ed. (McGraw-Hill, New York, 2000).

H. Cruse, Trends Neurosci. 13, 15 (1990).

H. Cruse, T. Kindermann, M. Schumm, J. Dean, and J. Schmitz, Neural Networks 11, 1435 (1998).

G. Manganaro, P. Arena, and L. Fortuna, Cellular Neural Networks. Chaos, Complexity VLSI Processing (Springer-Verlag, Berlin, 1999).

J. Ayers, J. Witting, N.J. McGruer, C. Olcott, and D. Massa, in Proceedings International Symporium on Aqua Biomechanisms, edited by T. Wu and N. Kato (Tokai University, 2000).

P. Arena, L. Fortuna, and M. Branciforte, IEEE Trans. Circuits Systems I 46, 253 (1999).

G. Schöner, W.Y. Yiang, and J.A.S. Kelso, J. Theor. Biol. 142, 359 (1990).

J.J. Collins and I.N. Stewart, J. Nonlinear Sci. 3, 349 (1993).

J.J. Collins and I.N. Stewart, Biol. Cybern. 68, 287 (1993).

M. Golubitsky and I.N. Stewart, Arch. Rational Mech. Anal. 87, 107 (1985).

Theory and Application of Coupled Map Lattices, edited by K. Kaneko (Wiley, Chichester, 1993).

K. Kaneko and I. Tsuda, Complex Systems: Chaos and Beyond (Springer-Verlag, Berlin, 2001).

G.R. Pradhan, N. Chatterjee, and N. Gupte, Phys. Rev. E 65, 046227 (2002).

R. Carretero-Gonzalez, D.K. Arrowsmith, and F. Vivaldi, Phys. Rev. E 61, 1329 (2000).

N. Gupte, A. Sharma, and G.R. Pradhan, Physica A 318, 85 (2003).

D.G. Luchinsky, P.V.E. McClintok, and M.I. Dykman, Rep. Prog. Phys. 61, 889 (1998).

F. Moss and P.V.E. McClintok, Noise in Nonlinear Dynamical Systems (Cambridge University Press, Cambridge, 1989), Vol. 3.

E. del Rio, J.R. Sanmartin, and O. Lopez-Rebollal, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 225 (1998).

D. Ruswisch, M. Bode, D. Volkov, and E. Volkov, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 1969 (1999).

E. Sanchez and M.A. Matias, Phys. Rev. E 57, 6184 (1998).

See, e.g., M. Toda, Theory of Nonlinear Lattices (Springer-Verlag, Berlin, 1981).

R. Hirota and K. Suzuki, Procs. IEEE 61, 1483 (1973).

A.C. Singer and A.V. Oppenheim, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 571 (1999).

N. Islam, J.P. Singh, and K. Steiglitz, J. Appl. Phys. 62, 689 (1987).

Y. Okada, S. Watanabe, and H. Tanaka, J. Phys. Soc. Jpn. 59, 2647 (1990) .

T. Kuusela and J. Hietarinta, Phys. Rev. Lett. 62, 700 (1989).

V.I. Nekorkin and M.G. Velarde, Synergetic Phenomena in Active Lattices. Patterns, Waves, Solitons, Chaos (Springer-Verlag, Berlin, 2002).

Lord Rayleigh, The Theory of Sound (Dover, New York, 1945), Vol. 1, Chap 3, p. 81.

V.A. Makarov, W. Ebeling, and M.G. Velarde, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 1075 (2000).

V.A. Makarov, E. del Río, W. Ebeling, and M.G. Velarde, Phys. Rev. E 64, 036601 (2001).

P. Horowitz and W. Hill, The Art of Electronics (Cambridge University Press, Cambridge, 1987).

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, New York, 1985).

Deposited On:25 Oct 2012 08:09
Last Modified:28 Jun 2016 14:05

Repository Staff Only: item control page