  We analyse the entanglement dynamics in a nonlinear Kerr-like coupler
interacting with external environment. Whenever the reservoir is in a thermal
vacuum state the entanglement (measured by concurrence for a two-qubit system)
exhibits regular oscillations of decreasing amplitude. In contrast, for thermal
reservoirs we can observe dark periods in concurrence oscillations (which can
be called a "sudden death" of the entanglement) and the entanglement rebuild
(which can be named the "sudden birth" of entanglement). We show that these
features can be observed when we deal with 2-qubit system as well as $2\otimes
3$ system.
