  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.
