Self-organization of periodicity hubs and spirals in a high resolution parameter space from the two-level model on semi-insulating GaAs
Semi-insulating Gallium Arsenide (SI-GaAs) samples experimentally show, under high electric fields and even at room temperature, negative differential conductivity in N-shaped form (NNDC). In recent work [1], we proposed a physical model, the two-valley model, which describes electrical conduction in SI-GaAs. The model is based on the minimal set of generation-recombination (g-r) equations for two valleys inside of the conduction band, and an equation for the drift velocity as a function of the applied electric field, that covers the physical properties of the nonlinear electrical conduction of the SI-GaAs system. The model generated theoretically the NNDC region for the first time and the nonlinear dynamics were investigated in this region by building of high-resolution parameter-space of the periodicity using a Periodicity-Detection routine [2]. In the parameter-space we observed too many self-organized periodic structures embedded in the chaotic regions, like as a ``shrimp" shaped in a spiral form, that forms a ``snail shell". This structure established a direct communication between the windows in order within chaotic regions, producing new routes of bifurcation. The snail structure show three regions where the shrimp shape rotated around a focal point, called periodicity hubs, with intricate connections between different shrimps.
The purpose of this work is to further develop our recent study and we focus on periodicity hubs. Such hubs shows focal points where your localization are associated with the generation recombination rate. In the present model the coefficients of g-r processes, like as impact ionization and field enhanced trapping, depend on the electric field. Our results shows the impact when a small variations on some parameter of the coefficients g-r can causes on position of the focal points and consequently over all self-organized periodic structure around them. Our results show that the position of the focal points and the structures of the periodic hubs have dependence with the change of the coefficients g-r. The stable and unstable hubs and many mergers between shrimps with different periodicity are presented.
[1] da Silva, S. L., Viana, E. R., de Oliveira, A. G., Ribeiro, G. M. and da Silva, R. L. - Int. J. Bifurcation Chaos 25, 1530004 (2015).
[2] Viana, E. R., Rubinger, R. M., Albuquerque, H. A., Dias, F. O., de Oliveira, A. G. and Ribeiro., G. M. - Nonlinear Dyn. 67, 385-392 (2012).