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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.