  We derive a system of cosmological equations for a braneworld with induced
curvature which is a junction between several bulk spaces. The permutation
symmetry of the bulk spaces is not imposed, and the values of the fundamental
constants, and even the signatures of the extra dimension, may be different on
different sides of the brane. We then consider the usual partial case of two
asymmetric bulk spaces and derive an exact closed system of scalar equations on
the brane. We apply this result to the cosmological evolution on such a brane
and describe its various partial cases.
