Hydraulic system, excavator, and control method of excavator

A hydraulic system comprising:

• a main hydraulic valve that is constituted by an open circuit that includes a main pump, a working equipment cylinder, a main valve that controls inflow of hydraulic oil from the main pump to the working equipment cylinder, and a tank to which the hydraulic oil that has flowed out of the working equipment cylinder is ejected via the main valve;
• a swing hydraulic circuit that is constituted by a closed circuit that includes a swing pump, a swing motor, and a neutral hold valve that controls passing of the hydraulic oil between the swing pump and the swing motor;
• a back pressure valve that is disposed on a tank flow passage between the main valve and the tank, and adjusts back pressure of the main valve;
• a warming-up flow passage that is disposed around a spool of the neutral hold valve;
• a supply flow passage that connects an upstream portion of the tank flow passage between the main valve and the back pressure valve to an entrance port of the warming-up flow passage;
• and
• an ejection flow passage that connects a downstream portion of the tank flow passage between the back pressure valve and the tank to an exit port of the warming-up flow passage.