Right now is the perfect time of year, plants are sucking nutrients into their roots for the winter. Herbicide in the sap gets into the roots and kills the whole plant.
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I'm going to guess, regardless of the chemical you use.. The most efficient time window will produce the most efficient control...
I do know I have seen someone go through a growth of woody invasive plants with a disc or sub soil shank... I believe there thinking was to break up the root system of how this plant spreads..
NOT a good idea as it seemed every cut end of the root system put up a new plant shortly or the next year.. Most of these types of invasive, un wanted require the multi step control of cut and chemical, for best results..