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Nonstandard Farey sequences in a realistic diode map

Technical Report:

Abstract

We study a realistic coupled map system, modelling a p - i - n diode structure. As we vary the parameter corresponding to the (scaled) external potential in the model, the dynamics goes through a flip bifurcation and then a Hopf bifurcation, and as the parameter is increased further, we find evidence of a sequence of mode locked windows embedded in the quasiperiodic motion, with periodic attractors whose winding numbers p = p/q, are given by a Farey series. The interesting thing about this Farey sequence is that it is generated between two parent attractors with p = 2/7 and 2/8, where 2/8 implies two distinct coexisting attractors with p = 1/4, and the correct series is obtained only when we use parent winding number 2/8 and not 1/4. So unlike a regular Farey tree, p and q need not be relatively prime here, p = 2 x p/2 x q is permissible, where such attractors are actually comprised of two coexisting attractors with p = p/q. We also checked that the positions and widths of these windows exhibit well defined power law scaling. When the potential is increased further, the Farey windows still provide a ``skeleton`` for the dynamics,  More>>
Publication Date:
Jun 01, 1991
Product Type:
Technical Report
Report Number:
IC-91/112
Reference Number:
SCA: 665200; PA: AIX-22:081918; SN: 91000608971
Resource Relation:
Other Information: PBD: Jun 1991
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; SEMICONDUCTOR DIODES; DYNAMICS; ATTRACTORS; NONLINEAR PROBLEMS; 665200; SOLID-STATE PLASMA
OSTI ID:
10105105
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE92609282; TRN: XA9129637081918
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
21 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Perez, G, Sinha, S, and Cerdeira, H. Nonstandard Farey sequences in a realistic diode map. IAEA: N. p., 1991. Web.
Perez, G, Sinha, S, & Cerdeira, H. Nonstandard Farey sequences in a realistic diode map. IAEA.
Perez, G, Sinha, S, and Cerdeira, H. 1991. "Nonstandard Farey sequences in a realistic diode map." IAEA.
@misc{etde_10105105,
title = {Nonstandard Farey sequences in a realistic diode map}
author = {Perez, G, Sinha, S, and Cerdeira, H}
abstractNote = {We study a realistic coupled map system, modelling a p - i - n diode structure. As we vary the parameter corresponding to the (scaled) external potential in the model, the dynamics goes through a flip bifurcation and then a Hopf bifurcation, and as the parameter is increased further, we find evidence of a sequence of mode locked windows embedded in the quasiperiodic motion, with periodic attractors whose winding numbers p = p/q, are given by a Farey series. The interesting thing about this Farey sequence is that it is generated between two parent attractors with p = 2/7 and 2/8, where 2/8 implies two distinct coexisting attractors with p = 1/4, and the correct series is obtained only when we use parent winding number 2/8 and not 1/4. So unlike a regular Farey tree, p and q need not be relatively prime here, p = 2 x p/2 x q is permissible, where such attractors are actually comprised of two coexisting attractors with p = p/q. We also checked that the positions and widths of these windows exhibit well defined power law scaling. When the potential is increased further, the Farey windows still provide a ``skeleton`` for the dynamics, and within each window there is a host of other interesting dynamical features, including multiple forward and reverse Feigenbaum trees. (author). 15 refs, 7 figs.}
place = {IAEA}
year = {1991}
month = {Jun}
}