A hybrid model for chaotic front dynamics: From semiconductors to water tanks

TL;DR

This paper introduces a hybrid tank model approach to analyze chaotic front dynamics in nonlinear systems, demonstrated on semiconductor superlattices, revealing complex patterns and bifurcation scenarios through analytical methods.

Contribution

The paper develops a general hybrid tank model framework for studying front propagation with global constraints, applicable to diverse physical systems including semiconductors and water tanks.

Findings

Chaotic behavior explained by tank models

Bifurcation scenario characterized by a modified tent map

Analytical results on chaos emergence in the model

Abstract

We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the electron accumulation and depletion fronts shows complex spatio-temporal patterns, including chaos. We show that this behavior may be elegantly explained by a tank model, for which analytical results on the emergence of chaos are available. In particular, for the case of three tanks the bifurcation scenario is characterized by a modified version of the one-dimensional iterated tent-map.