Supersymmetric multiple basin attractors

We explain that supersymmetric attractors in general have several critical points due to the algebraic nature of the stabilization equations. We show that the critical values of the cosmological constant of the AdS(5) vacua a re given by the topological (moduli-independent) formulae analogous to the entropy of the d = 5 supersymmetric black holes. In one-moduli case critica l points with positive definite metric and gauge couplings exist under cond ition that the central charge changes the sign from one critical point to t he other. We have found several families of Z(2)-symmetric critical points where the central charge has equal absolute values but opposite signs in tw o attractor points. We present examples of interpolating solutions and disc uss their generic features.