  An overdamped dynamical system, biased by an external constant force, does
not exhibit negative mobility. However, when the system is coupled to its copy,
negative mobility can arise. We show it by the example of an experimentally
realizable system of two coupled resistively shunted Josephson junctions. The
first junction is dc-biased by a constant current and ac-driven by an unbiased
harmonic current. In the proposed setup one can control the transport
properties of the second junction by manipulating the first junction only. We
demonstrate that the second junction can exhibit both absolute negative
resistance (ANR) near zero bias and negative resistance in the non-linear
regimes (NNR). These anomalous transport features occur for restricted windows
of the coupling constant.
