Chaotic motion of space charge wavefronts in semiconductors under   time-independent voltage bias
  A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples, appropriate contact resistivity and applied voltage - such that the sample is biased in a regime of negative differential resistance - we find chaos in the propagation of nonlinear fronts (charge monopoles of alternating sign) of electric field. The chaos is always low-dimensional, but has a complex spatial structure; this behavior can be interpreted using a finite dimensional asymptotic model in which the front (charge monopole) positions and the electrical current are the only dynamical variables. 
I. R. Cantalapiedra, M. J. Bergmann, L. L. Bonilla, S. W. Teitsworth