  We study the effects of dissipation on electron transport in a semiconductor
superlattice with an applied bias voltage and a magnetic field that is tilted
relative to the superlattice axis.In previous work, we showed that although the
applied fields are stationary,they act like a THz plane wave, which strongly
couples the Bloch and cyclotron motion of electrons within the lowest miniband.
As a consequence,the electrons exhibit a unique type of Hamiltonian chaos,
which creates an intricate mesh of conduction channels (a stochastic web) in
phase space, leading to a large resonant increase in the current flow at
critical values of the applied voltage. This phase-space patterning provides a
sensitive mechanism for controlling electrical resistance. In this paper, we
investigate the effects of dissipation on the electron dynamics by modifying
the semiclassical equations of motion to include a linear damping term. We
demonstrate that even in the presence of dissipation,deterministic chaos plays
an important role in the electron transport process. We identify mechanisms for
the onset of chaos and explore the associated sequence of bifurcations in the
electron trajectories. When the Bloch and cyclotron frequencies are
commensurate, complex multistability phenomena occur in the system. In
particular, for fixed values of the control parameters several distinct stable
regimes can coexist, each corresponding to different initial conditions. We
show that this multistability has clear, experimentally-observable, signatures
in the electron transport characteristics.
