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We study the effects of dissipation and noise on chaotic electron dynamics, which accompany charge transport in semiconductor superlattices with an applied bias voltage and a tilted magnetic field. We consider the evolution of different chaotic trajectories as decoherence increases, and show that below a critical level of the dissipation rate, dissipative chaos plays an important role in the electron transport. However, by increasing the dissipation rate above the critical level, chaoticdoi:10.12693/aphyspola.116.733 fatcat:cjmdsdwjm5f6pht4lugqr3d23y