  We study numerically the effects of time delay in networks of delay-coupled
excitable FitzHugh Nagumo systems with dissipation. The generation of periodic
self-sustained oscillations and its threshold are analyzed depending on the
dissipation of a single neuron, the delay time, and random initial conditions.
The peculiarities of spatiotemporal dynamics of time-delayed bidirectional
ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of
local and nonlocal coupling topology between the nodes, and a first-order
nonequilibrium phase transition to synchrony is established. It is shown that
the emergence of oscillatory activity in delay-coupled FitzHugh-Nagumo neurons
is observed for smaller values of the coupling strength as the dissipation
parameter decreases. This can provide the possibility of controlling the
spatiotemporal behavior of the considered neuronal networks. The observed
effects are quantified by plotting distributions of the maximal Lyapunov
exponent and the global order parameter in terms of delay and coupling
strength.
