I have lots of Jerusalem artichokes... once you have a little, you rapidly have a lot, it spreads fast. Every fall, I pull ALL the JA's out of the flower bed they are in. The small tubers that break off and are accidentally left behind are plenty to repopulate for the next year.
But be careful about substituting them for potatoes. The JA's are extremely gas producing. For this reason they are sometimes known as "fartichokes."
Here's what wiki says about them:
Jerusalem artichokes are easy to cultivate, which tempts gardeners to simply leave them completely alone to grow. However, the quality of the edible tubers degrades unless the plants are dug up and replanted in fertile soil. This can be a chore, as even a small piece of tuber will grow if left in the ground, making the hardy plant a potential weed. In fact the plant can be pernicious. It can be destructive to other plants and gardens and can overtake huge areas if left untamed. Commercial fields growing sunchoke which then change to other vegetables or crops often must be eradicated with roundup (sometimes twice) to stop the spread of the sun-chokes. Each sunchoke root can make an additional 75 to as many as 200 tubers by fall end.
he tubers are sometimes used as a substitute for potatoes: they have a similar consistency, and in their raw form have a similar texture, but a sweeter, nuttier flavor; raw and sliced thinly, they are fit for a salad. The carbohydrates give the tubers a tendency to become soft and mushy if boiled, but they retain their texture better when steamed. The inulin cannot be broken down by the human digestive system, which can cause flatulence and, in some cases, gastric pain. Gerard's Herbal, printed in 1621, quotes the English planter John Goodyer on Jerusalem artichokes:
"which way soever they be dressed and eaten, they stir and cause a filthy loathsome stinking wind within the body, thereby causing the belly to be pained and tormented, and are a meat more fit for swine than men."
MyHoney has trouble with gas anyway. After I served the JA's (mixed with potatoes), two days in a row, I had to promise NEVER to do that again. Made me pretty jet propelled too, and I usually do not have trouble like that.
I have heard that if you do not harvest them until after fall frost, the inulin starts to break down and they aren't as bad.