  One of the most enigmatic phenomena related to solar activity is the
so-called Maunder minimum phase. It consists of the lowest sunspot's counting
ever registered for the Sun, and never so far confirmed for other stars. Since
the spectroscopic observations of stellar activity at the Mount Wilson
Observatory, the solar analog HD43587 has shown a very low and apparently
invariant activity level, which makes it a Maunder minimum candidate. We
analyze the chromospheric activity evolution of HD43587 and its evolutive
status, intending to unravel the reasons for this low and flat activity. We use
an activity measurements dataset available in the literature, and compute the
activity S-index from HARPS and NARVAL spectra, to infer a cycle period.
Besides, we analyze the CoRoT light-curve of HD43587, and apply gyrochronology
and activity calibrations, to determine its rotation period. Finally, based on
an evolutionary model and the inferred rotation period, we use the EULAG-MHD
code to perform global MHD simulations of HD43587 with the aim of getting some
insights about its dynamo process. We confirm the almost flat activity profile,
with a cycle period $P_{\mathrm{cyc}} = 10.44\pm3.03$ yrs deduced from the
S-index time series, and a long-term trend that might be a period larger than
50 yrs. It was impossible to define a rotation period from the light-curve,
however gyrochronology and activity calibrations allow to infer an indirect
estimate of $\overline{P}_{\mathrm{rot}} = 22.6 \pm 1.9$ d. Furthermore, the
MHD simulations confirm an oscillatory dynamo with a cycle period in good
agreement with the observations and a low level of surface magnetic activity.
We conclude that this object might be experiencing a "natural" decrease in
magnetic activity as a consequence of its age. Nevertheless, the possibility
that HD43587 is in a Maunder minimum phase cannot be ruled out.
