Do the planets in the HD 34445 system really exist?

In 2010 the first planet was discovered around star HD 34445. Recently, another five planets were announced orbiting the same star. It is a rather dense multiplanet system with some of its planets having separations of fractions of an au and minimum masses ranging from Neptune to sub-Jupiter ones. Given the number of planets and the various uncertainties in their masses and orbital elements, the HD 34445 planetary system is quite interesting as there is the potential for mean motion and secular resonances that could render the outcome of its dynamical evolution and fate an open question. In this paper we investigate the dynamical stability of the six-planet system in order to check the validity of the orbital solution acquired. This is achieved by a series of numerical experiments, where the dynamical evolution of the system is tested on different time-scales. We vary the orbital elements and masses of the system within the error ranges provided. We find that for a large area of the parameter space we can produce stable configurations and therefore conclude it is very likely that the HD 34445 planetary system is real. Some discussion about the potential habitability of the system is also done.