Nonstandard Farey sequences in a realistic diode map

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 an exchange of stability bifurcation and a Hopf bifurcation. When the parameter is increased further, we find evidence of a sequence of mode-locked windows embedded in the quasi-periodic motion. These periodic attractors can be ordered according to a Farey tree that is generated between two parent fractions 2/7 and 2/8, where 2/8 implies two distinct coexisting attractors with ρ=¼, and the correct structure is obtained only when we use the parent fraction 2/8. So, unlike a regular Farey tree, here numerator and denominator of the Farey fractions need not be relative primes. 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.