  Many complex networks are known to exhibit sudden transitions between
alternative steady states with contrasting properties. Such a sudden transition
demonstrates a network's resilience, which is the ability of a system to
persist in the face of perturbations. Most of the research on network
resilience has focused on the transition from one equilibrium state to an
alternative equilibrium state. Although the presence of non-equilibrium
dynamics in some nodes may advance or delay sudden transitions in networks and
give early warning signals of an impending collapse, it has not been studied
much in the context of network resilience. Here we bridge this gap by studying
a neuronal network model with diverse topologies, in which non-equilibrium
dynamics may appear in the network even before the transition to a resting
state from an active state in response to environmental stress deteriorating
their external conditions. We find that the percentage of uncoupled nodes
exhibiting non-equilibrium dynamics plays a vital role in determining the
network's transition type. We show that a higher proportion of nodes with
non-equilibrium dynamics can delay the tipping and increase networks'
resilience against environmental stress, irrespective of their topology.
Further, predictability of an upcoming transition weakens, as the network
topology moves from regular to disordered.
