We report on a series of experiments on the dynamics of spontaneous emission controlled nanolasers. The laser cavity is a photonic-crystal slab cavity, embedding self-assembled quantum dots as gain material. The implementation of cavity electrodynamics effects increases the large signal modulation bandwidth significantly, with measured modulation speeds of the order of $10\mathrm{GHz}$ while keeping an extinction ratio of $19\mathrm{dB}$ . A linear transient wavelength shift is reported, corresponding to a chirp of less than 100 pm for a $35\mathrm{ps}$ laser pulse. We observe that the chirp characteristics are independent of the repetition rate of the laser up to $10\mathrm{GHz}$ .