  The suppression of oscillations in coupled systems may lead to several
unwanted situations, which requires a suitable treatment to overcome the
suppression. In this paper, we show that the environmental coupling in the
presence of direct interaction, which can suppress oscillation even in a
network of identical oscillators, can be modified by introducing a feedback
factor in the coupling scheme in order to restore the oscillation. We inspect
how the introduction of the feedback factor helps to resurrect oscillation from
various kind of death states. We numerically verify the resurrection of
oscillations for two paradigmatic limit cycle systems, namely Landau-Stuart and
Van der Pol oscillators and also in generic chaotic Lorenz oscillator. We also
study the effect of parameter mismatch in the process of restoring oscillation
for coupled oscillators.
