## 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,
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## 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}

}

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}

}