Could even be a dodgy Rectifier/Regulator.Drain the carbs on to white kitchen toweling or tissue to see if there is sediment in the bowls.Check the fuel filter.Check the fuel flow from the pump.Check the Air filterCheck/test plug capsCheck PlugsCheck/test coilsBalance the carbs Set idle speed Set TPSIf all check out change the rectifier/regulator
It probably is and the first time I came across it was on my sons 2003 model 600, I swapped over everything one item at the time from my 600 and when we swapped out the Rectifier/Regulator the problem disappeared.There was no other symptom and it happened suddenly.Spoke to a number of mechanics I know and they never came across anything like it. I have come across another one since on a 1999 model 600 and it was the first thing I changed, problem gone.They are different rectifier, look the same with same connectors, but are very different.
The 2002-2003 has a higher charging rate from the alternator and it is better able to control the higher output.There would be little point of swapping a working older one with the newer one as the alternator does not have the higher output, but if an older one fails the 2002- 2003 will work fine as a replacement or a one from the 2001 to 2006 FZS1000.The 2001 to 2005 FZS1000 one is the same model as the 2002 to 2003 FZS600, but the wires are longer on the 1000 one.
The carb is changing over from one set of jets to another at that rev range point and it only takes very slight pressure change from dirty air filter to mess it up totally. Once you get the revs higher it will be running slightly rich but not enough to give misfires or significant power loss