We consider the process of resonant electron tunneling through a doubl
e-barrier potential, taking into account nonlinear dynamical effects g
enerated by charge accumulation in the interbarrier space. We use the
perturbation approach of Davydov and Ermakov, which was developed for
investigating intrinsic bistability in resonant tunneling. For incomin
g electron flow, which is modulated slowly in time, we show that the r
esulting nonlinear dynamics can become chaotic, with the chaos describ
ed (because of the open nature of the system) by a strange attractor.
We determine the conditions for the existence of this strange attracto
r and estimate characteristic experimental parameters for its observat
ion.