We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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This paper deals with the problem of controlling the average state of a large-scale linear network to a constant reference value. We design an output-feedback controller such that no information about state vector or system matrices is needed. For this controller to have arbitrary positive gains, it is sufficient that only a sign condition on system matrices should be satisfied. To assure that the states of the network are close to the average state, the problem of deviation minimization is solved in addition, using a novel extremum seeking algorithm.