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injectors or plugs can definitely cause what you are experiencing although all failing at once would be unusual. It might make sense to change a few out to see if the faults are then gone from those cylinders. if they remain then you are looking more likely at an ecu/electrical issue.
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I would suspect a possible issue with the wiring to the injectors/plugs or possibly at the connection to the ecu as the pins are very delicate. Additionally, it would make sense to check battery and alternator output voltage under different conditions to ensure they are within spec as this could also cause an issue like you have. Please do not forget to CLICK ON a positive rating