  Magnetic fields of exoplanets are important in shielding the planets from
cosmic rays and interplanetary plasma. Due to the interaction with the
electrons from their host stars, the exoplanetary magnetospheres are predicted
to have both cyclotron and synchrotron radio emissions, of which neither has
been definitely identified in observations yet. As the coherent cyclotron
emission has been extensively studied in literatures, here we focus on the
planetary synchrotron radiation with bursty behaviors (i.e., radio flares)
caused by the outbreaks of energetic electron ejections from the host star. Two
key parameters of the bursty synchrotron emissions, namely the flux density and
burst rate, and two key features namely the burst light curve and frequency
shift, are predicted for star - hot Jupiter systems. The planetary orbital
phase - burst rate relation is also considered as the signature of star-planet
interactions (SPI). As examples, previous X-ray and radio observations of two
well studied candidate systems, HD 189733 and V830 \tau, are adopted to predict
their specific burst rates and fluxes of bursty synchrotron emissions for
further observational confirmations. The detectability of such emissions by
current and upcoming radio telescopes shows that we are at the dawn of
discoveries.
