  We investigate spatio-temporal patterns occurring in a two-layer multiplex
network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented
by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the
coupling between the layers is smaller than that within the layers, can have a
significant impact on the dynamics of the neural network. We develop control
strategies based on weak multiplexing and demonstrate how the desired state in
one layer can be achieved without manipulating its parameters, but only by
adjusting the other layer. We find that for coupling range mismatch weak
multiplexing leads to the appearance of chimera states with different shapes of
the mean velocity profile for parameter ranges where they do not exist in
isolation. Moreover, we show that introducing a coupling strength mismatch
between the layers can suppress chimera states with one incoherent domain
(one-headed chimeras) and induce various other regimes such as in-phase
synchronization or two-headed chimeras. Interestingly, small intra-layer
coupling strength mismatch allows to achieve solitary states throughout the
whole network.
