  We present a new coupling scheme to control spatio-temporal patterns and
chimeras on 1-d and 2-d lattices and random networks of discrete dynamical
systems. The scheme involves coupling with an external lattice or network of
damped systems. When the system network and external network are set in a
feedback loop, the system network can be controlled to a homogeneous steady
state or synchronized periodic state with suppression of the chaotic dynamics
of the individual units. The control scheme has the advantage that its design
does not require any prior information about the system dynamics or its
parameters and works effectively for a range of parameters of the control
network. We analyze the stability of the controlled steady state or amplitude
death state of lattices using the theory of circulant matrices and
Routh-Hurwitz's criterion for discrete systems and this helps to isolate
regions of effective control in the relevant parameter planes. The conditions
thus obtained are found to agree well with those obtained from direct numerical
simulations in the specific context of lattices with logistic map and Henon map
as on-site system dynamics. We show how chimera states developed in an
experimentally realizable 2-d lattice can be controlled using this scheme. We
propose this mechanism can provide a phenomenological model for the control of
spatio-temporal patterns in coupled neurons due to non-synaptic coupling with
the extra cellular medium. We extend the control scheme to regulate dynamics on
random networks and adapt the master stability function method to analyze the
stability of the controlled state for various topologies and coupling
strengths.
