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.
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