Three states of a magnetic island are observed when the magnetic shear at the rational surface is modified using inductive current associated with the neutral beam current drive in the Large Helical Device. One state is the healed magnetic island with a zero island width. The second state is the saturated magnetic island with partial flattening of the T(e) profile. The third state is characterized by the global flattening of the T(e) profile in the core region. As the plasma assumes each of the three states consecutively through a bifurcation process a clear hysteresis in the relation between the size of the magnetic island and the magnetic shear is observed.