  We study the atomic gas content and the central stellar mass concentration
for a sample of almost 1500 nearby galaxies to investigate the nature of
starbursts and the influence of galaxy-galaxy interactions on star formation
(SF). We used a sample of catalogued interacting and non-interacting galaxies
in the S$^4$G survey - along with archival HI gas masses, stellar masses
($M_{\ast}$), and SF rates from $IRAS$ far-infrared fluxes - and calculate
depletion times and gas fractions. We traced the central stellar mass
concentration from the inner slope of the stellar component of the rotation
curves. Starbursts are defined as galaxies with a factor $>4$ enhanced SF rate
relative to a control sample of non-interacting galaxies which are $\pm 0.2$
dex in stellar mass and $\pm 1$ in $T$-type. Starbursts are mainly early-type
($T\lesssim 5$), massive spiral galaxies ($M_{\ast}\gtrsim 10^{10}M_{\odot}$)
that are not necessarily interacting. For a given stellar mass bin, starbursts
are characterised by lower gas depletion times, similar gas fractions, and
larger central stellar mass concentrations than non-starburst galaxies. The
global distributions of gas fraction and gas depletion time are not
statistically different for interacting and non-interacting galaxies. However,
in the case of currently merging galaxies, the median gas depletion time is a
factor of $0.4 \pm 0.2$ that of control sample galaxies, and their SF rates are
a factor of $1.9 \pm 0.5$ enhanced, even though the median gas fraction is
similar. Starbursts present long-lasting SF in the circumnuclear regions that
causes an enhancement of the central stellar density at $z\approx0$ in both
interacting and non-interacting systems. Starbursts have low gas depletion
timescales, yet similar gas fractions as normal main-sequence galaxies. Galaxy
mergers cause a moderate enhancement of the SF efficiency (Abridged).
