Recurrent bursts of toroidicity induced Alfvén eigenmodes (TAEs) are reproduced with a Fokker-Planck-MHD simulation where a fast ion source and slowing down are incorporated self-consistently.The bursts take place at regular time intervals and the behaviours of all the TAEs are synchronized. The fast ion transport due to TAE activity spatially broadens the classicalfast ion distribution and significantly reduces its peak value.Only a small change of the distribution takes place with each burst, leadingto loss of a small fraction of the fast ions.The system stays close to the marginal stability state established through the interplay of the fast ion source, slowing down and TAE activity.