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We present a new coupling scheme to control spatio-temporal patterns andchimeras on 1-d and 2-d lattices and random networks of discrete dynamicalsystems. The scheme involves coupling with an external lattice or network ofdamped systems. When the system network and external network are set in afeedback loop, the system network can be controlled to a homogeneous steadystate or synchronized periodic state with suppression of the chaotic dynamicsof the individual units. The control scheme has the advantage that its designdoes not require any prior information about the system dynamics or itsparameters and works effectively for a range of parameters of the controlnetwork. We analyze the stability of the controlled steady state or amplitudedeath state of lattices using the theory of circulant matrices andRouth-Hurwitz's criterion for discrete systems and this helps to isolateregions of effective control in the relevant parameter planes. The conditionsthus obtained are found to agree well with those obtained from direct numericalsimulations in the specific context of lattices with logistic map and Henon mapas on-site system dynamics. We show how chimera states developed in anexperimentally realizable 2-d lattice can be controlled using this scheme. Wepropose this mechanism can provide a phenomenological model for the control ofspatio-temporal patterns in coupled neurons due to non-synaptic coupling withthe extra cellular medium. We extend the control scheme to regulate dynamics onrandom networks and adapt the master stability function method to analyze thestability of the controlled state for various topologies and couplingstrengths.

Novel coupling scheme to control dynamics of coupled discrete systems