  We explore how entanglement of a general bipartite system evolves when one
subsystem undergoes the action of an arbitrary noisy channel. It is found that
the dynamics of entanglement for general bipartite systems under the influence
of such channel is determined by the channel's action on the maximally
entangled state, which includes as a special case the results for two-qubit
systems [Nature Physics 4, 99 (2008)]. In particular, for multi-qubit or
qubit-qudit systems, we get a general factorization law for evolution equation
of entanglement with one qubit being subject to a noisy channel. Our results
can help the experimental characterization of entanglement dynamics.
