In this paper searches for flaring astrophysical neutrino sources and sources with periodic emission with the IceCube neutrino telescope are presented. In contrast to time integrated searches, where steady emission is assumed, the analyses presented here look for a time dependent signal of neutrinos using the information from the neutrino arrival times to enhance the discovery potential. A search was performed for correlations between neutrino arrival times and directions as well as neutrino emission following time dependent lightcurves, sporadic emission or periodicities of candidate sources. These include active galactic nuclei, soft $gamma$-ray repeaters, supernova remnants hosting pulsars, micro-quasars and X-ray binaries. The work presented here updates and extends previously published results to a longer period that covers four years of data from 2008 April 5 to 2012 May 16 including the first year of operation of the completed 86-string detector. The analyses did not find any significant time dependent point sources of neutrinos and the results were used to set upper limits on the neutrino flux from source candidates.
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