High Resolution Parameter-Space from a Two-Level Model on Semi-Insulating GaAs

Abstract

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. Schöll was not capable to generate the NNDC curve for SI-GaAs, in this work we have 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.

Extensive Numerical Study and Circuitry Implementation of the Watt Governor Model

“…The results presented here, corroborate the generic nature of those SPSs, independently of the systems' nonlinearity. For example, these SPSs are observed in piecewise-linear [de Sousa et al, 2016;Hoff et al, 2014], polynomial [Celestino et al, 2014;Silva et al, 2015;, and exponential [Cardoso et al, 2009] nonlinearities. Here, both quadratic and trigonometric nonlinearity are considered, since the model studied is derived from a mechanical (steam) engine through the Newton's Second Law of motion.…”