Try cleaning your Idle Air Control stepper motor and the passageway for it on the throttle body. Also, do you have any ECU diagnostic capability? If not, this thread will help:
http://www.chinariders.net/showthrea...t=29467&page=2
Post #16 gives you all the information for what is required. Also, I've corrected the links for the OBD 6 pin to 16 pin cable, so you can use them to buy what you need. Once you get the necessary gear and set it up, record a data log of your RX3 while it's running and post to Google Drive. We'll be able to read it and see exactly what your bikes Delphi MT-05 ECU is seeing, which will help diagnose the problem.