High Resolution Parameter Space from a 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). Since the most consolidated model for n-GaAs, namely, "the model", proposed by E. Scholl was not capable to generate the NNDC curve for SI-GaAs, in this work we proposed an alternative model. The model proposed, "the two-valley model" is based on the minimal set of generation recombination 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 "two valley model" was capable to generate theoretically the NNDC region for the first time, and with that, we were able to build a high resolution parameter-space of the periodicity (PSP) using a Periodicity-Detection (PD) routine. In the parameter space were observed self-organized periodic structures immersed in chaotic regions. The complex regions are presented in a "shrimp" shape rotated around a focal point, which forms in large-scale a "snail shell" shape, with intricate connections between different "shrimps". The knowledge of detailed information on parameter spaces is crucial to localize wide regions of smooth and continuous chaos. 
S. L. da Silva, E. R. Viana, A. G. de Oliveira, G. M. Ribeiro and R.   L. da Silva
nlin.AO cond-mat.mes-hall nlin.PS physics.comp-ph