Starting with a subexcitable net of FitzHugh-Nagumo elements additive parameter-variability (diversity, heterogeneity)
is able to induce pattern formation. The patterns are most coherent for an intermediate variability
strength. Multiplicative variability is able to induce a transition to an excitable net dynamics. In the present
paper the interplay of additive and multiplicative variability in subexcitable nets of FitzHugh-Nagumo elements
is examined. It is shown that the diversity in the net leads to a coherent dynamics. The net can generate
excitation waves, which spread through the whole net. Furthermore the response of the net with variability to
a stochastic forcing (additive noise) is studied. Increasing the strength of the additive noise the net without
variability shows spatiotemporal stochastic resonance. The noise strength for which the pattern formation sets
in and the shape of the resonance curve strongly depend on the strength of the additive variability. For large
values the effect of spatiotemporal stochastic resonance is destroyed. The coherence of the patterns in presence
of additive noise and additive variability can be maximized by applying additionally multiplicative variability.
The influence of time-delayed feedback on the dynamics of a net of oscillatory FitzHugh-Nagumo elements is
investigated. We show that the global oscillation of the net can be suppressed (amplitude death) and excitable
network dynamics can be restored via time-delayed feedback for a properly chosen delay time. We investigate
the influence of local and global feedback and the dependence of the amplitude death regime on the parameters
of the feedback signal. Furthermore the influence of the coupling strength on the transition from the global
oscillation to excitable network dynamics is studied. Starting with a net, whose global oscillation is suppressed,
weak additive noise can induce excitation waves (noise-induced pattern formation), a fingerprint of excitable network dynamics.
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