No, you cannot make barbecue directly on an induction stove. Induction stoves use electromagnetic fields to heat the cookware directly, rather than heating the surface of the stove. Barbecuing typically involves grilling food over an open flame or hot coals, which is not possible on an induction stove.
However, you can use an induction cooktop or stove in combination with other equipment to achieve a similar result. For instance, you could use an indoor electric grill or a stovetop grill pan on the induction stove to cook your barbecue-style food. These specialized equipment options are designed to provide the grill marks and flavors associated with barbecuing, even indoors.
It's important to note that while you can simulate the flavors and textures of barbecue indoors, it may not be exactly the same as traditional outdoor barbecue cooking. The smoky flavor that comes from outdoor grilling with charcoal or wood chips is challenging to replicate indoors.